http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Ansley+Marks 2026-04-30T04:02:15Z User contributions MediaWiki 1.42.7 http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=9784 2015-12-03T06:03:59Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ==Real World Examples==<br /> <br /> ===Magnetic Resonance Imaging===<br /> <br /> A good analogy for the way that a Magnetic Resonance Imaging (MRI) works is a gyroscope. To start off with a little background, the way that an MRI works is that all the hydrogen atoms in your body are aligned by using strong magnetic fields. Once these hydrogen atoms are aligned, similar to how a compass's needle is aligned, radio waves can be sent into the body and signals are created from the way the photons emit the radio waves. <br /> <br /> Identical to gyroscopes, the hydrogen nucleus rotates about its own axis at a particular frequency. The strength and direction of the magnetic field can effect the direction and angular speed of these rotating protons in the nuclei. By controlling the direction and rotation speed, the location of the hydrogen nucleus can be deduced and thus helping the process of creating images.<br /> <br /> ===Aviation===<br /> <br /> Gyroscopes offer two functions in aircraft. The first is rigidity in space, which means that the gyroscope will resist any attempt to change the direction of the axis. This is useful when the plane makes turns, throwing the plane off its natural horizontal. The gyroscope acts as a &quot;fake horizon&quot;, which orientates the plane back to its natural position. The technical term for this gyroscope contraption is an attitude indicator. <br /> <br /> The second function of gyroscopes in planes is precession. In this context, this means that any perpendicular force applied to a gyroscope's axis of rotation will manifest itself 90° further along the axis of rotation. This property is useful because the amount of banking before a turn can be determined. If the gyroscope was oriented with the longitudinal axis of the plane, then only the rate of turn could be determined instead of the amount of bank on the aircraft.<br /> <br /> ==Connectedness==<br /> This topic is interesting because gyroscopes have held the fascination of pretty much anyone that has ever seen one in motion including myself. Although the explanation that I gave was a simplified version of a gyroscope which only processes and doesn't nutate, there are many other complex mathematical models of the complicated motion of gyroscopes. Many papers and even books have been written on the subject of gyroscopes, and they have baffled nobel prize winners such as Niels Bohr and famous physicists alike. Gyroscopes are connected to my major because they are huge in industrial manufacturing of numerous materials. We use some sort of gyroscope in our everyday lives from cars to airplanes and other mechanical equipments. <br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> https://www.youtube.com/watch?v=ty9QSiVC2g0<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> Science Learning: http://sciencelearn.org.nz/Contexts/See-through-Body/Sci-Media/Video/So-how-does-MRI-work<br /> <br /> Quora: https://www.quora.com/What-the-function-of-gyroscopes-in-airplane <br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=9781 2015-12-03T06:02:31Z

<p>Ansley Marks: /* References */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ==Real World Examples==<br /> <br /> ===Magnetic Resonance Imaging===<br /> <br /> A good analogy for the way that a Magnetic Resonance Imaging (MRI) works is a gyroscope. To start off with a little background, the way that an MRI works is that all the hydrogen atoms in your body are aligned by using strong magnetic fields. Once these hydrogen atoms are aligned, similar to how a compass's needle is aligned, radio waves can be sent into the body and signals are created from the way the photons emit the radio waves. <br /> <br /> Identical to gyroscopes, the hydrogen nucleus rotates about its own axis at a particular frequency. The strength and direction of the magnetic field can effect the direction and angular speed of these rotating protons in the nuclei. By controlling the direction and rotation speed, the location of the hydrogen nucleus can be deduced and thus helping the process of creating images.<br /> <br /> ===Aviation===<br /> <br /> Gyroscopes offer two functions in aircraft. The first is rigidity in space, which means that the gyroscope will resist any attempt to change the direction of the axis. This is useful when the plane makes turns, throwing the plane off its natural horizontal. The gyroscope acts as a &quot;fake horizon&quot;, which orientates the plane back to its natural position. The technical term for this gyroscope contraption is an attitude indicator. <br /> <br /> The second function of gyroscopes in planes is precession. In this context, this means that any perpendicular force applied to a gyroscope's axis of rotation will manifest itself 90° further along the axis of rotation. This property is useful because the amount of banking before a turn can be determined. If the gyroscope was oriented with the longitudinal axis of the plane, then only the rate of turn could be determined instead of the amount of bank on the aircraft.<br /> <br /> ==Connectedness==<br /> This topic is interesting because gyroscopes have held the fascination of pretty much anyone that has ever seen one in motion including myself. Although the explanation that I gave was a simplified version of a gyroscope which only processes and doesn't nutate, there are many other complex mathematical models of the complicated motion of gyroscopes. Many papers and even books have been written on the subject of gyroscopes, and they have baffled nobel prize winners such as Niels Bohr and famous physicists alike. Gyroscopes are connected to my major because they are huge in industrial manufacturing of numerous materials. We use some sort of gyroscope in our everyday lives from cars to airplanes and other mechanical equipments. <br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> Science Learning: http://sciencelearn.org.nz/Contexts/See-through-Body/Sci-Media/Video/So-how-does-MRI-work<br /> <br /> Quora: https://www.quora.com/What-the-function-of-gyroscopes-in-airplane <br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=9778 2015-12-03T06:01:53Z

<p>Ansley Marks: /* Aviation */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ==Real World Examples==<br /> <br /> ===Magnetic Resonance Imaging===<br /> <br /> A good analogy for the way that a Magnetic Resonance Imaging (MRI) works is a gyroscope. To start off with a little background, the way that an MRI works is that all the hydrogen atoms in your body are aligned by using strong magnetic fields. Once these hydrogen atoms are aligned, similar to how a compass's needle is aligned, radio waves can be sent into the body and signals are created from the way the photons emit the radio waves. <br /> <br /> Identical to gyroscopes, the hydrogen nucleus rotates about its own axis at a particular frequency. The strength and direction of the magnetic field can effect the direction and angular speed of these rotating protons in the nuclei. By controlling the direction and rotation speed, the location of the hydrogen nucleus can be deduced and thus helping the process of creating images.<br /> <br /> ===Aviation===<br /> <br /> Gyroscopes offer two functions in aircraft. The first is rigidity in space, which means that the gyroscope will resist any attempt to change the direction of the axis. This is useful when the plane makes turns, throwing the plane off its natural horizontal. The gyroscope acts as a &quot;fake horizon&quot;, which orientates the plane back to its natural position. The technical term for this gyroscope contraption is an attitude indicator. <br /> <br /> The second function of gyroscopes in planes is precession. In this context, this means that any perpendicular force applied to a gyroscope's axis of rotation will manifest itself 90° further along the axis of rotation. This property is useful because the amount of banking before a turn can be determined. If the gyroscope was oriented with the longitudinal axis of the plane, then only the rate of turn could be determined instead of the amount of bank on the aircraft.<br /> <br /> ==Connectedness==<br /> This topic is interesting because gyroscopes have held the fascination of pretty much anyone that has ever seen one in motion including myself. Although the explanation that I gave was a simplified version of a gyroscope which only processes and doesn't nutate, there are many other complex mathematical models of the complicated motion of gyroscopes. Many papers and even books have been written on the subject of gyroscopes, and they have baffled nobel prize winners such as Niels Bohr and famous physicists alike. Gyroscopes are connected to my major because they are huge in industrial manufacturing of numerous materials. We use some sort of gyroscope in our everyday lives from cars to airplanes and other mechanical equipments. <br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> Science Learning: http://sciencelearn.org.nz/Contexts/See-through-Body/Sci-Media/Video/So-how-does-MRI-work<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=9710 2015-12-03T05:47:22Z

<p>Ansley Marks: /* References */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ==Real World Examples==<br /> <br /> ===Magnetic Resonance Imaging===<br /> <br /> A good analogy for the way that a Magnetic Resonance Imaging (MRI) works is a gyroscope. To start off with a little background, the way that an MRI works is that all the hydrogen atoms in your body are aligned by using strong magnetic fields. Once these hydrogen atoms are aligned, similar to how a compass's needle is aligned, radio waves can be sent into the body and signals are created from the way the photons emit the radio waves. <br /> <br /> Identical to gyroscopes, the hydrogen nucleus rotates about its own axis at a particular frequency. The strength and direction of the magnetic field can effect the direction and angular speed of these rotating protons in the nuclei. By controlling the direction and rotation speed, the location of the hydrogen nucleus can be deduced and thus helping the process of creating images.<br /> <br /> ===Aviation===<br /> <br /> ==Connectedness==<br /> This topic is interesting because gyroscopes have held the fascination of pretty much anyone that has ever seen one in motion including myself. Although the explanation that I gave was a simplified version of a gyroscope which only processes and doesn't nutate, there are many other complex mathematical models of the complicated motion of gyroscopes. Many papers and even books have been written on the subject of gyroscopes, and they have baffled nobel prize winners such as Niels Bohr and famous physicists alike. Gyroscopes are connected to my major because they are huge in industrial manufacturing of numerous materials. We use some sort of gyroscope in our everyday lives from cars to airplanes and other mechanical equipments. <br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> Science Learning: http://sciencelearn.org.nz/Contexts/See-through-Body/Sci-Media/Video/So-how-does-MRI-work<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=9708 2015-12-03T05:46:24Z

<p>Ansley Marks: /* MRI */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ==Real World Examples==<br /> <br /> ===Magnetic Resonance Imaging===<br /> <br /> A good analogy for the way that a Magnetic Resonance Imaging (MRI) works is a gyroscope. To start off with a little background, the way that an MRI works is that all the hydrogen atoms in your body are aligned by using strong magnetic fields. Once these hydrogen atoms are aligned, similar to how a compass's needle is aligned, radio waves can be sent into the body and signals are created from the way the photons emit the radio waves. <br /> <br /> Identical to gyroscopes, the hydrogen nucleus rotates about its own axis at a particular frequency. The strength and direction of the magnetic field can effect the direction and angular speed of these rotating protons in the nuclei. By controlling the direction and rotation speed, the location of the hydrogen nucleus can be deduced and thus helping the process of creating images.<br /> <br /> ===Aviation===<br /> <br /> ==Connectedness==<br /> This topic is interesting because gyroscopes have held the fascination of pretty much anyone that has ever seen one in motion including myself. Although the explanation that I gave was a simplified version of a gyroscope which only processes and doesn't nutate, there are many other complex mathematical models of the complicated motion of gyroscopes. Many papers and even books have been written on the subject of gyroscopes, and they have baffled nobel prize winners such as Niels Bohr and famous physicists alike. Gyroscopes are connected to my major because they are huge in industrial manufacturing of numerous materials. We use some sort of gyroscope in our everyday lives from cars to airplanes and other mechanical equipments. <br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8611 2015-12-02T23:40:35Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ==Real World Examples==<br /> <br /> ===MRI===<br /> <br /> ===Aviation===<br /> <br /> ==Connectedness==<br /> This topic is interesting because gyroscopes have held the fascination of pretty much anyone that has ever seen one in motion including myself. Although the explanation that I gave was a simplified version of a gyroscope which only processes and doesn't nutate, there are many other complex mathematical models of the complicated motion of gyroscopes. Many papers and even books have been written on the subject of gyroscopes, and they have baffled nobel prize winners such as Niels Bohr and famous physicists alike. Gyroscopes are connected to my major because they are huge in industrial manufacturing of numerous materials. We use some sort of gyroscope in our everyday lives from cars to airplanes and other mechanical equipments. <br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8602 2015-12-02T23:28:13Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> Since the direction of the rotational angular momentum of the rotor around the support is constantly changing direction, the rate of change of the rotational angular momentum can be written as:<br /> <br /> '''LrotΩ'''<br /> <br /> Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:<br /> <br /> '''Ω = τCM/Lrot = ''r''Mg/''I''ω '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> Gyroscope History: http://www.gyroscopes.org/history.asp<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8595 2015-12-02T23:15:46Z

<p>Ansley Marks: /* History */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Gyroscopes have been around for nearly 200 years. The first person to discover the gyroscope was Johann Bohnenberger in 1817 at the University of Tubingen. However, Bohnenberger was not credited with the discovery of the gyroscope. The French scientist Jean Bernard Leon Foucault (1826-1864) coined the term &quot;gyroscope&quot; and ended up with being credited for the discovery of a gyroscope. Thanks to his experiments with the gyroscope, they started to become mainstream and studied by many other physicists. In the early 20th century, gyroscopes were first used in boats and eventually in aircraft. Gyroscopes have been modified and tweaked to suit many purposes that are widely used today mainly as stabilizers.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8585 2015-12-02T23:06:36Z

<p>Ansley Marks: /* See also */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8584 2015-12-02T23:05:43Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the [http://dictionary.reference.com/browse/precession precession] motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/precession<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8581 2015-12-02T23:03:53Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> http://dictionary.reference.com/browse/nutation<br /> <br /> https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=8579 2015-12-02T23:02:36Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, [http://dictionary.reference.com/browse/nutation nutation] (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Compass and Gyroscope: Integrating Science and Politics for the Environment<br /> <br /> Mathematical model for gyroscope effects: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4915651<br /> <br /> YouTube video on gyroscope procession: https://www.youtube.com/watch?v=ty9QSiVC2g0 <br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7536 2015-12-02T03:05:06Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A view of the gyroscope from the side with all the forces labeled.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7488 2015-12-02T02:52:33Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.611.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Figure11.611.png&diff=7484 2015-12-02T02:52:02Z

<p>Ansley Marks: </p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Figure11.61.png&diff=7479 2015-12-02T02:51:20Z

<p>Ansley Marks: Ansley Marks uploaded a new version of &amp;quot;File:Figure11.61.png&amp;quot;</p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Figure11.61.png&diff=7472 2015-12-02T02:50:31Z

<p>Ansley Marks: </p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7457 2015-12-02T02:48:15Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. [[File:figure11.61.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7445 2015-12-02T02:45:08Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. <br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P'' | '''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7440 2015-12-02T02:44:37Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. <br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;. <br /> <br /> There is also a translational angular momentum of the rotor processing about the support. This can be modeled by finding the magnitude of the position vector crossed with the momentum.<br /> <br /> '''Lsupport = |''R'' x ''P''|'''<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7424 2015-12-02T02:40:34Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device. The linear momentum of the gyroscope is then Ω''P''. <br /> <br /> Since the rotor is processing about the support, there must be a perpendicular force ''f'' exerted by the support such that Ω''P'' = ''f'', where ''P'' is equal to ''M(Ωr)''. Thus, ''f'' = ''Mr''&lt;math&gt;Ω^2&lt;/math&gt;<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7347 2015-12-02T02:20:01Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. <br /> <br /> If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7344 2015-12-02T02:18:50Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''V''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7337 2015-12-02T02:16:44Z

<p>Ansley Marks: /* A Mathematical Model */</p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> Where the rotational angular momentum points horizontal to the rotor. <br /> <br /> The Lrot,r will always change direction as the rotor rotates about the support. The rotor processes about the support with an angular velocity Ω, which is constant in magnitude and direction. If Ω is known, then the velocity of the center of mass of the rotor device can be derived using the following relationship:<br /> <br /> '''Ω = ''v''cm/''r'''''<br /> <br /> Where ''r'' is equal to the distance from the support to the center of mass of the rotor device.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7300 2015-12-02T02:01:37Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7298 2015-12-02T02:00:55Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic1.png|200px|thumb|left|alt text]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyropic1.png&diff=7297 2015-12-02T02:00:25Z

<p>Ansley Marks: A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.</p> <hr /> <div>A gyroscope processing in the x,z plane with the y-axis positioned upwards along the vertical support.</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyropic.png&diff=7290 2015-12-02T01:57:10Z

<p>Ansley Marks: A gyroscope processing in the x,z plane with the y axis positioned along the vertical support.</p> <hr /> <div>A gyroscope processing in the x,z plane with the y axis positioned along the vertical support.</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7287 2015-12-02T01:55:42Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyropic.png|200px|thumb|left|alt text]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot,r = Iω'''<br /> <br /> <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7284 2015-12-02T01:53:41Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyroprocess1.png|200px|thumb|left|alt text]]<br /> <br /> To start off with, the gyroscope's rotor rotates about its own axis with an angular velocity of ω and has a moment of inertia ''I''. Thus, the rotational angular momentum of the rotor can be modeled as:<br /> <br /> '''Lrot = Iω'''<br /> <br /> <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7272 2015-12-02T01:43:53Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyroprocess1.png|200px|thumb|left|alt text]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyroprocess1.png&diff=7269 2015-12-02T01:43:18Z

<p>Ansley Marks: </p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyroprocess.png&diff=7268 2015-12-02T01:42:31Z

<p>Ansley Marks: Ansley Marks uploaded a new version of &amp;quot;File:Gyroprocess.png&amp;quot;</p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyroprocess.png&diff=7264 2015-12-02T01:41:04Z

<p>Ansley Marks: </p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7263 2015-12-02T01:40:18Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyroprocess.png|200px|thumb|left|alt text]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyroprecess.png&diff=7259 2015-12-02T01:39:10Z

<p>Ansley Marks: </p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7252 2015-12-02T01:37:32Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File: gyroprecess.png]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyroprecession.png&diff=7249 2015-12-02T01:36:08Z

<p>Ansley Marks: Ansley Marks uploaded a new version of &amp;quot;File:Gyroprecession.png&amp;quot;</p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7242 2015-12-02T01:33:05Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File: gyroprecession.png]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=File:Gyroprecession.png&diff=7240 2015-12-02T01:32:11Z

<p>Ansley Marks: </p> <hr /> <div></div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7239 2015-12-02T01:31:18Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File: gyroprecession.jpg]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7229 2015-12-02T01:27:34Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyroprecession.jpg]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7228 2015-12-02T01:27:12Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a gyroscopic effect can be observed. <br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> When the spinning axis of a gyroscope is placed on a support, a gyroscopic effect is observed. The gyroscope bobs up and down--nutation--and rotates about the support--precession. For the sake of simplifying the mathematical equations for a gyroscope's motion, nutation (the upwards and downwards movement of the rotor) will be ignored. We will only look at the precession motion of the gyroscope. <br /> <br /> [[File:gyroprecession.gif]]<br /> <br /> To start off with, <br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7179 2015-12-02T01:04:55Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7176 2015-12-02T01:04:31Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: /* Angular Momentum */ ]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7171 2015-12-02T01:03:30Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> <br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7167 2015-12-02T01:02:55Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes become a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes come in all different forms with varying parts. The main component of a gyroscope is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. If the spinning axle of a gyroscope is placed on a support, then a complex motion can be observed. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html<br /> Wikipedia: https://en.wikipedia.org/wiki/Gyroscope<br /> <br /> [[Category: Angular Momentum]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7127 2015-12-02T00:47:07Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes are a fascinating device when in motion and can be explained using the angular momentum principle. Gyroscopes can come in all different forms with varying parts. The main component of a gyroscope, however, is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7125 2015-12-02T00:46:33Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes are a fascinating device that can be explained using the angular momentum principle. Gyroscopes can come in all different forms with varying parts. The main component of a gyroscope, however, is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Ansley Marks http://www.physicsbook.gatech.edu/index.php?title=Gyroscopes&diff=7123 2015-12-02T00:45:36Z

<p>Ansley Marks: </p> <hr /> <div><br /> An explanation by Ansley Marks<br /> <br /> A gyroscope is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself.<br /> <br /> [[File: gyro.gif]]<br /> <br /> ==The Main Idea==<br /> <br /> Although insignificant looking and seemingly uninteresting when still, gyroscopes are a fascinating device that can be explained with the angular momentum principle. Gyroscopes can come in all different forms with varying parts. The main component of a gyroscope, however, is a spinning wheel or a disk mounted on an axle. Typically gyroscopes contain a suspended rotor inside three rings called gimbals. In order to ensure that little torque is applied to the inside rotor, the gimbals are mounted on high quality bearing surfaces, allowing free movement of the spinning wheel in the middle. These types of gyroscopes with multiple gimbals are useful for stabilization because the wheels can change direction without affecting the inner rotor. The motion of a gyroscope will be modeled and explained further on in this page. <br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> Oxford Dictionaries: http://www.oxforddictionaries.com/us/definition/american_english/gyroscope<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Ansley Marks