Physics Book - User contributions [en]

Angular Impulse

2015-12-08T16:42:54Z

Kdelgado8:

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===
A point on a solid disk on the xy-plane with radius 5 cm rotates with a constant initial frequency of 5 revolutions per second. The mass of the disk is 2 kilograms. Someone applies a force to the wheel suddenly, giving it a constant angular acceleration of 6 rad/s^2 for 3 seconds. Use the angular impulse to find the final angular velocity.
====Solution====
This problem involves several steps. It is clear that if we are going to find the angular impulse, we either need to find the torque times the time interval or the change in angular velocity.
For finding the angular velocity, we are given the initial frequency and radius of the disk, so since angular velocity is equal to 2 times pi times the frequency, we get 10⋅pi rad/s for the initial angular velocity.

Now that we have the initial angular velocity, we need to somehow find the final angular velocity. Since angular impulse is the change in angular velocity, we can use this to determine what the final angular velocity is.

Angular impulse is equal to torque times time. Remember that the torque is equal to the moment of inertia times angular acceleration. We are told that we are dealing with a solid disk, so we need to find the moment of inertia which is mr^2, or 2 kg ⋅ (.05 m)^2, which gives us a moment of inertia of .005 kg ⋅ m^2. Since we are given the angular acceleration and have the moment of inertia, we can now find the torque, which is equal to (.005 kg ⋅ m^2) ⋅ (6 rad/s^2), or .03 N⋅m.

Since we now have the torque and the duration that it is applied is given, we can now find the angular impulse. We multiple the torque by time, or (.03 N⋅m) ⋅ (3 s), and get .09 N⋅m⋅s as our angular impulse.

Now that we have the angular impulse, we can find the final angular velocity. Before that, we need our initial angular momentum, which we get by multiplying the initial angular velocity by the moment of inertia. This gives us .05 pi or about .157 N⋅m⋅s. We have the angular impulse, so we add this to the initial angular momentum and get our final angular momentum, about .247 N⋅m⋅s. Then we divide by the moment of inertia to get the final angular velocity, about 49.42 rad/s.

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

== See also ==
[http:///www.physicsbook.gatech.edu/Torque Torque]

[http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle The Angular Momentum Principle]

[http://www.physicsbook.gatech.edu/The_Moments_of_Inertia Moments of Inertia]

[http://www.physicsbook.gatech.edu/Angular_Velocity Angular Velocity]

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T16:42:23Z

Kdelgado8: /* Difficult */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===
A point on a solid disk on the xy-plane with radius 5 cm rotates with a constant initial frequency of 5 revolutions per second. The mass of the disk is 2 kilograms. Someone applies a force to the wheel suddenly, giving it a constant angular acceleration of 6 rad/s^2 for 3 seconds. Use the angular impulse to find the final angular velocity.
====Solution====
This problem involves several steps. It is clear that if we are going to find the angular impulse, we either need to find the torque times the time interval or the change in angular velocity.
For finding the angular velocity, we are given the initial frequency and radius of the disk, so since angular velocity is equal to 2 times pi times the frequency, we get 10⋅pi rad/s for the initial angular velocity.

Now that we have the initial angular velocity, we need to somehow find the final angular velocity. Since angular impulse is the change in angular velocity, we can use this to determine what the final angular velocity is.

Angular impulse is equal to torque times time. Remember that the torque is equal to the moment of inertia times angular acceleration. We are told that we are dealing with a solid disk, so we need to find the moment of inertia which is mr^2, or 2 kg ⋅ (.05 m)^2, which gives us a moment of inertia of .005 kg ⋅ m^2. Since we are given the angular acceleration and have the moment of inertia, we can now find the torque, which is equal to (.005 kg ⋅ m^2) ⋅ (6 rad/s^2), or .03 N⋅m.

Since we now have the torque and the duration that it is applied is given, we can now find the angular impulse. We multiple the torque by time, or (.03 N⋅m) ⋅ (3 s), and get .09 N⋅m⋅s as our angular impulse.

Now that we have the angular impulse, we can find the final angular velocity. Before that, we need our initial angular momentum, which we get by multiplying the initial angular velocity by the moment of inertia. This gives us .05 pi or about .157 N⋅m⋅s. We have the angular impulse, so we add this to the initial angular momentum and get our final angular momentum, about .247 N⋅m⋅s. Then we divide by the moment of inertia to get the final angular velocity, about 49.42 rad/s.

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==
[http:///www.physicsbook.gatech.edu/Torque Torque]

[http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle The Angular Momentum Principle]

[http://www.physicsbook.gatech.edu/The_Moments_of_Inertia Moments of Inertia]

[http://www.physicsbook.gatech.edu/Angular_Velocity Angular Velocity]

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T11:02:02Z

Kdelgado8: /* Difficult */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===
====Solution====

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==
[http:///www.physicsbook.gatech.edu/Torque Torque]

[http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle The Angular Momentum Principle]

[http://www.physicsbook.gatech.edu/The_Moments_of_Inertia Moments of Inertia]

[http://www.physicsbook.gatech.edu/Angular_Velocity Angular Velocity]

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T11:01:32Z

Kdelgado8: /* Examples */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==
[http:///www.physicsbook.gatech.edu/Torque Torque]

[http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle The Angular Momentum Principle]

[http://www.physicsbook.gatech.edu/The_Moments_of_Inertia Moments of Inertia]

[http://www.physicsbook.gatech.edu/Angular_Velocity Angular Velocity]

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:59:47Z

Kdelgado8: /* See also */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==
[http:///www.physicsbook.gatech.edu/Torque Torque]

[http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle The Angular Momentum Principle]

[http://www.physicsbook.gatech.edu/The_Moments_of_Inertia Moments of Inertia]

[http://www.physicsbook.gatech.edu/Angular_Velocity Angular Velocity]

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:59:37Z

Kdelgado8: /* See also */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==
[http:///www.physicsbook.gatech.edu/Torque Torque]

[http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle The Angular Momentum Principle]

[http://www.physicsbook.gatech.edu/The_Moments_of_Inertia Moments of Inertia]

[http://www.physicsbook.gatech.edu/Angular_Velocity Angular Velocity]

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:55:52Z

Kdelgado8: /* Solution */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5 N ⋅ m ⋅ s.

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:55:32Z

Kdelgado8: /* Simple */

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math> or <math display="inline">N⋅m⋅s</math>.

===A Computational Model===

Angular impulse is often used to update angular momentum when there is a torque acting on an object. Much like how force times time (impulse) is used to update momentum by adding it to an initial momentum in order to obtain the final momentum when the force is constant, angular impulse can also be used to find final angular momentum or final angular velocity. This can be done by adding angular impulse to an initial angular momentum in a while loop and setting that equal to the final angular momentum. Below is part of a simple code example of a while loop that will update the final angular momentum by adding angular impulse. The final angular momentum is angm_f, the initial angular momentum is angm_i, torquenet is the net torque, deltat is some pre-defined time step, and t is time.

[[File:Angm.png]]

In order to find final angular velocity, one could simply divide the final angular momentum by the moment of inertia (a constant) within the while loop after updating the final angular momentum (angm_f in the example) and before updating the time (t in the example).

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
The moment of inertia of an upright solid cylinder is 22.5 m ⋅ r^2. The cylinder is rotated from rest and has a final angular velocity of 5 rad/s. What is the angular impulse of the cylinder?

====Solution====
We are given the moment of inertia, final angular velocity, and deduce that the initial angular velocity is 0 rad/s since it began rotating from rest. As a result, we can find the angular velocity by multiplying the moment of inertia with the change in angular velocity, or 5 rad/s minus 0 rad/s times 22.5 m ⋅ r^2. This gives us the angular impulse, 112.5

===Middling===

A net force of 40 N is applied to the rim of a spinning wheel for 2 seconds. The radius of the wheel is 20 cm. Find the angular impulse that is applied to this wheel.

====Solution====
First, we need to find the torque acting on the wheel. Torque is equal to the applied force times the radius, or 40 N ⋅ .2 meters which equals 8 N ⋅ m.
Currently, we know the torque applied as well as the duration of its application. Therefore, we can find the angular impulse, which is the applied torque times the duration, or (8 N ⋅ m) ⋅ (2 s) which equals 16 N ⋅ m ⋅ s, the angular impulse.

===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

[http://webpages.charter.net/griche/pt/u8s2prb.htm Angular Impulse Practice]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:47:25Z

Kdelgado8: /* Solution */

Angular Impulse

2015-12-08T10:47:07Z

Kdelgado8: /* Units */

Angular Impulse

2015-12-08T10:44:04Z

Kdelgado8: /* See also */

Angular Impulse

2015-12-08T10:43:30Z

Kdelgado8: /* External links */

Angular Impulse

2015-12-08T10:43:23Z

Kdelgado8: /* External links */

Angular Impulse

2015-12-08T10:42:12Z

Kdelgado8: /* Middling */

Angular Impulse

2015-12-08T10:29:33Z

Kdelgado8: /* A Mathematical Model */

Angular Impulse

2015-12-08T10:28:33Z

Kdelgado8: /* A Computational Model */

File:Angm.png

2015-12-08T10:23:31Z

Kdelgado8:

Angular Impulse

2015-12-08T10:19:54Z

Kdelgado8: /* A Computational Model */

Angular Impulse

2015-12-08T10:10:02Z

Kdelgado8:

Angular Impulse

2015-12-08T10:09:27Z

Kdelgado8: /* External links */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[https://www.youtube.com/watch?v=KWrVvLxUhlA Angular Momentum Impulse Video]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:08:09Z

Kdelgado8: /* The Main Idea */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T10:00:45Z

Kdelgado8:

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T09:56:18Z

Kdelgado8: /* A Mathematical Model */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse indicates the direction that the system will rotate in (clockwise or counterclockwise).

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. If it is positive, it results in the system rotating in a counterclockwise direction. If it is negative, the system will rotate in a clockwise direction. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-08T09:51:03Z

Kdelgado8: /* Connectedness */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse indicates the direction that the system will rotate in (clockwise or counterclockwise).

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. If it is positive, it results in the system rotating in a counterclockwise direction. If it is negative, the system will rotate in a clockwise direction. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

<math>\Delta L = I\Delta\omega = I\omega_f - I\omega_i</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-06T04:49:34Z

Kdelgado8: /* Connectedness */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse indicates the direction that the system will rotate in (clockwise or counterclockwise).

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. If it is positive, it results in the system rotating in a counterclockwise direction. If it is negative, the system will rotate in a clockwise direction. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

<math>\Delta L = I\Delta\omega = I\omega_f - I\omega_i</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

#How is it connected to your major?
As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

#Is there an interesting industrial application?
Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels),

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-06T02:54:10Z

Kdelgado8: /* References */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse indicates the direction that the system will rotate in (clockwise or counterclockwise).

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. If it is positive, it results in the system rotating in a counterclockwise direction. If it is negative, the system will rotate in a clockwise direction. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

<math>\Delta L = I\Delta\omega = I\omega_f - I\omega_i</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>

Angular Impulse

2015-12-06T02:50:12Z

Kdelgado8: /* References */

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse indicates the direction that the system will rotate in (clockwise or counterclockwise).

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. If it is positive, it results in the system rotating in a counterclockwise direction. If it is negative, the system will rotate in a clockwise direction. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

The angular impulse is equal to the net cross product of a force vector, <math display="inline">\vec{F}</math>, applied at a particular location a vector distance <math display="inline">\vec{d}</math> from a pivot point times a specified time interval <math display="inline">\Delta t</math>. This is also equal to the net torque <math display="inline">\sum{\vec{\tau}}</math> times a specified time interval <math display="inline">\Delta t</math>.

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

<math>\Delta L = I\Delta\omega = I\omega_f - I\omega_i</math>

==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>

Angular Impulse

2015-12-06T02:44:03Z

Kdelgado8: /* A Mathematical Model */

Angular Impulse

2015-12-06T02:39:42Z

Kdelgado8: /* The Main Idea */

Angular Impulse

2015-12-06T02:38:37Z

Kdelgado8: /* Angular Momentum Principle */

Angular Impulse

2015-12-06T02:37:32Z

Kdelgado8: /* Angular Momentum Principle */

Angular Impulse

2015-12-06T02:36:22Z

Kdelgado8: /* Angular Momentum Principle */

File:Netangularimpulse.png

2015-12-06T02:35:46Z

Kdelgado8:

Angular Impulse

2015-12-06T02:34:21Z

Kdelgado8: /* A Mathematical Model */

Angular Impulse

2015-12-06T02:24:51Z

Kdelgado8:

Angular Impulse

2015-12-06T01:38:08Z

Kdelgado8: /* A Mathematical Model */

Claimed by Katherine Delgado.

Short Description of Topic

==The Main Idea==

Angular impulse is the torque acting over some time interval or the change in angular momentum.

===A Mathematical Model===

<math>\Delta L = \sum{\tau}*\Delta t</math>

<math>\Delta L = I\Delta\omega = I\omega_f - I\omega_i</math>

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Angular Impulse

2015-12-05T19:36:00Z

Kdelgado8:

Claimed by Katherine Delgado.

Short Description of Topic

==The Main Idea==

Angular impulse is the torque acting over some time interval or the change in angular momentum.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Angular Impulse

2015-12-05T19:21:14Z

Kdelgado8:

Claimed by Katherine Delgado.

PLEASE DO NOT EDIT THIS PAGE. COPY THIS TEMPLATE AND PASTE IT INTO A NEW PAGE FOR YOUR TOPIC.

Short Description of Topic

==The Main Idea==

State, in your own words, the main idea for this topic

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Edmond Becquerel

2015-12-05T19:10:30Z

Kdelgado8: Blanked the page

Edmond Becquerel

2015-12-05T19:01:48Z

Kdelgado8: Created page with "Claimed by Katherine Delgado."

Claimed by Katherine Delgado.

Angular Impulse

2015-12-05T19:01:06Z

Kdelgado8: Created page with "Claimed by Katherine Delgado."

Claimed by Katherine Delgado.