Angular Impulse - Revision history

Amohammed87 at 04:03, 1 April 2024

2024-04-01T04:03:56Z

← Older revision		Revision as of 00:03, 1 April 2024
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	Another way to derive angular impulse is by using 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>.		Another way to derive angular impulse is by using 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 \vec{L} = \sum{(\vec{d}\times\vec{F})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

Amanivannan7: /* Angular Momentum Principle */

2016-11-28T04:53:56Z

Angular Momentum Principle

← Older revision		Revision as of 00:53, 28 November 2016
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	Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.		Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.
	This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant, which theoretically should equal 0 since the system experiences no changes in angular momentum.		This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant, which theoretically should equal 0 since the system experiences no changes in angular momentum.

	'''Example: Spring through the air'''		'''Example: Spring through the air'''
	A spring, initially stretched past its equilibrium, thrown in the air with an initial spin would have constant angular momentum even though the spring would oscillate back and forth. When the spring is compressed, moment of inertia would decrease (meaning it takes less to rotate the spring) so the angular velocity would increase. When the spring is stretched out, making it harder to rotate, the moment of inertia would increase consequently decreasing angular velocity. At any time during its path, the angular momentum is conserved, which goes to show that angular impulse is 0 since no net torque was applied on the object.		A spring, initially stretched past its equilibrium, thrown in the air with an initial spin would have constant angular momentum even though the spring would oscillate back and forth. When the spring is compressed, moment of inertia would decrease (meaning it takes less to rotate the spring) so the angular velocity would increase. When the spring is stretched out, making it harder to rotate, the moment of inertia would increase consequently decreasing angular velocity. At any time during its path, the angular momentum is conserved, which goes to show that angular impulse is 0 since no net torque was applied on the object.

	'''Example: skater'''		'''Example: skater'''
	When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.		When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.

Amanivannan7: /* Connectedness */

2016-11-28T04:49:21Z

Connectedness

← Older revision		Revision as of 00:49, 28 November 2016
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	==Connectedness==		==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~~.		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. Knowing the angular impulse of an object us can help us understand how the net torque is changing over time. As we took the integral of torque over time for impulse, we can take the derivative of the impulse graph at any point to figure out the torque applied at that current time. This is useful in calculations of electron spin, and particle analysis.

	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.		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.

Amanivannan7 at 04:02, 28 November 2016

2016-11-28T04:02:36Z

← Older revision		Revision as of 00:02, 28 November 2016
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	'''Example: skater'''		'''Example: skater'''
	When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.		When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.
	[[File:Conservation.gif~~\|300~~]]
			[[File:Conservation.gif]]

	==== Units ====		==== Units ====

Amanivannan7 at 03:44, 28 November 2016

2016-11-28T03:44:21Z

← Older revision		Revision as of 23:44, 27 November 2016
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	'''Example: skater'''		'''Example: skater'''
	When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.		When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.
	[[File:Conservation.gif]]		[[File:Conservation.gif\|300]]

	==== Units ====		==== Units ====
Line 83:		Line 83:
	==Connectedness==		==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.		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.		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.

Amanivannan7: /* Angular Momentum Principle */

2016-11-28T03:42:05Z

Angular Momentum Principle

← Older revision		Revision as of 23:42, 27 November 2016
Line 34:		Line 34:
	Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.		Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.
	This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant, which theoretically should equal 0 since the system experiences no changes in angular momentum.		This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant, which theoretically should equal 0 since the system experiences no changes in angular momentum.
	'''[[Example: Spring through the air]]'''		'''Example: Spring through the air'''
	A spring, initially stretched past its equilibrium, thrown in the air with an initial spin would have constant angular momentum even though the spring would oscillate back and forth. When the spring is compressed, moment of inertia would decrease (meaning it takes less to rotate the spring) so the angular velocity would increase. When the spring is stretched out, making it harder to rotate, the moment of inertia would increase consequently decreasing angular velocity. At any time during its path, the angular momentum is conserved, which goes to show that angular impulse is 0 since no net torque was applied on the object.		A spring, initially stretched past its equilibrium, thrown in the air with an initial spin would have constant angular momentum even though the spring would oscillate back and forth. When the spring is compressed, moment of inertia would decrease (meaning it takes less to rotate the spring) so the angular velocity would increase. When the spring is stretched out, making it harder to rotate, the moment of inertia would increase consequently decreasing angular velocity. At any time during its path, the angular momentum is conserved, which goes to show that angular impulse is 0 since no net torque was applied on the object.
	'''''Example: skater'''''		'''Example: skater'''
			When a skater goes to do a triple axle in the air, he/she tucks in initially to get maximum angular velocity with decreased moment of inertia to gather as much angular momentum as he/she can before jumping into the air and gracefully spiralling back down. While midair, he/she may choose to tuck in more to increase the number of spins, or decide to splay out limbs to increase inertia to slow down. The whole time, angular impulse is 0 since he/she maintains the angular momentum he/she started with due to the momentum principle.
			[[File:Conservation.gif]]

	==== Units ====		==== Units ====

Amanivannan7: /* Angular Momentum Principle */

2016-11-28T03:35:04Z

Angular Momentum Principle

← Older revision		Revision as of 23:35, 27 November 2016
Line 33:		Line 33:
	Both sides are equal to the net angular impulse for a system.		Both sides are equal to the net angular impulse for a system.
	Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.		Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.
	This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant.		This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant, which theoretically should equal 0 since the system experiences no changes in angular momentum.
			'''[[Example: Spring through the air]]'''
			A spring, initially stretched past its equilibrium, thrown in the air with an initial spin would have constant angular momentum even though the spring would oscillate back and forth. When the spring is compressed, moment of inertia would decrease (meaning it takes less to rotate the spring) so the angular velocity would increase. When the spring is stretched out, making it harder to rotate, the moment of inertia would increase consequently decreasing angular velocity. At any time during its path, the angular momentum is conserved, which goes to show that angular impulse is 0 since no net torque was applied on the object.
			'''''Example: skater'''''

	==== Units ====		==== Units ====

Amanivannan7: Conservation of momentum

2016-11-28T02:10:27Z

Conservation of momentum

← Older revision		Revision as of 22:10, 27 November 2016
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	==== Angular Momentum Principle ====		==== Angular Momentum Principle ====
	The angular momentum principle directly involves angular impulse as shown in the ~~image~~ below:		The angular momentum principle directly involves angular impulse as shown in the equation below:
	~~[[File:Netangularimpulse.png\|60 ]]~~

			''ΔL = τ-netΔt''
	Both sides are equal to the net angular impulse for a system.		Both sides are equal to the net angular impulse for a system.
			Thus, angular momentum is a measure of how much or little torque is applied to an object over a period of time. When a system is in the air, it is safe to say that the angular momentum of that object is constant because the only force acting on it is gravity, since the object cannot push or pull against anything to produce external torque.
			This constant angular momentum of an object spinning in midair is a perfect example of the momentum principle, or moreso the conservation of momentum. Even though the system may experience a spectrum of inertias throughout its midair flight, the gravitational force on it is constant, so the sum of torques is also constant.

	==== Units ====		==== Units ====

Amanivannan7: /* Angular Momentum Principle */

2016-11-28T02:02:19Z

Angular Momentum Principle

← Older revision		Revision as of 22:02, 27 November 2016
Line 29:		Line 29:
	==== Angular Momentum Principle ====		==== Angular Momentum Principle ====
	The angular momentum principle directly involves angular impulse as shown in the image below:		The angular momentum principle directly involves angular impulse as shown in the image below:
	[[File:Netangularimpulse.png\|~~300~~ ]]		[[File:Netangularimpulse.png\|60 ]]

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

Amanivannan7 at 02:02, 28 November 2016

2016-11-28T02:02:02Z

← Older revision		Revision as of 22:02, 27 November 2016
Line 29:		Line 29:
	==== Angular Momentum Principle ====		==== Angular Momentum Principle ====
	The angular momentum principle directly involves angular impulse as shown in the image below:		The angular momentum principle directly involves angular impulse as shown in the image below:
	[[File:Netangularimpulse.png]]		[[File:Netangularimpulse.png\|300 ]]

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