Gyroscopes - Revision history

Thomas Rodriguez at 18:21, 3 December 2024

2024-12-03T18:21:30Z

← Older revision		Revision as of 14:21, 3 December 2024
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	'''[]'''		'''__'''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Thomas Rodriguez at 18:21, 3 December 2024

2024-12-03T18:21:01Z

← Older revision		Revision as of 14:21, 3 December 2024
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	''''''		'''[]'''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Thomas Rodriguez at 18:20, 3 December 2024

2024-12-03T18:20:02Z

← Older revision		Revision as of 14:20, 3 December 2024
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	'''~~Claimed by...~~'''		''''''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Thomas Rodriguez at 18:19, 3 December 2024

2024-12-03T18:19:49Z

← Older revision		Revision as of 14:19, 3 December 2024
Line 1:		Line 1:
	''''''		'''Claimed by...'''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Thomas Rodriguez at 18:19, 3 December 2024

2024-12-03T18:19:33Z

← Older revision		Revision as of 14:19, 3 December 2024
Line 1:		Line 1:
	'''~~Claimed by Thomas Rodriguez, work in progress (Fall 2024)~~'''		''''''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Thomas Rodriguez at 03:58, 29 November 2024

2024-11-29T03:58:23Z

← Older revision		Revision as of 23:58, 28 November 2024
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	'''Claimed by ~~Avirath Dodabele~~ (Fall ~~2019~~)'''		'''Claimed by Thomas Rodriguez, work in progress (Fall 2024)'''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Aviphys at 19:23, 24 November 2019

2019-11-24T19:23:59Z

← Older revision		Revision as of 15:23, 24 November 2019
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	Therefore, the spinning disk made of aluminum would precess faster.		Therefore, the spinning disk made of aluminum would precess faster.

			===Middling===

			'''Problem:'''
			The axis of a gyroscope is tilted at an angle of 30° to the vertical. The rotor has a radius of 15 cm, mass 3 kg, moment of inertia 0.06 kg·m2, and spins on its axis at 30 rad/s. It is supported in a cage (not shown) in such a way that without an added weight it does not precess. Then a mass of 0.2 kg is hung from the axis at a distance of 18 cm from the center of the rotor.

			How long does it take for the gyroscope to make one complete precession?

			'''Answer:'''

			<math>Ω = \frac{\tau_{cm}}{L_{rot}}</math>

			<math> L_{rot} = I\omega </math>

			<math> L_{rot} = (0.06 kg * m^2)(30 rad/s) </math>

			<math> = 1.8 kgm^2s^-1</math>

			We must now consider the torque that is caused by the weight in the y direction

			<math> \tau_{cm} = mgrsin(30) </math>

			<math> = (0.2 kg) (9.8 m/s^2)(0.18 m)sin(30) </math>

			<math> = 0.1764 kg*m^2 </math>

			Now, we can calculate the angular speed of precession

			<math>Ω = \frac{0.1764 kgm^2}{1.8 kgm^2*s^-1}</math>

			<math> = 0.098 rad*s^-1 </math>

			<math> t = \frac{2\pi}{ Ω }</math>

			<math> = \frac{2\pi}{0.098 rad*s^-1 }</math>

			<math> = 64 seconds </math>

Aviphys at 02:35, 24 November 2019

2019-11-24T02:35:42Z

← Older revision		Revision as of 22:35, 23 November 2019
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	Without understanding the effects of gyroscopic precession, helicopters wouldn't fly and planes would crash.		Without understanding the effects of gyroscopic precession, helicopters wouldn't fly and planes would crash.
			==Problems==

			===Simple===

			'''Problem:''' Two gyroscopes are made exactly alike except that the spinning disk in one is made of low-density aluminum, whereas the disk in the other is made of high-density lead. If they have the same spin angular speeds and the same torque is applied to both, which gyroscope precesses faster?

			'''Answer:'''

			Precession Angular Speed:
			<math>Ω = \frac{\tau_{cm}}{I\omega}</math>

			Given:

			<math> \tau_{Aluminum} = \tau_{Lead}</math>

			<math> \omega_{Aluminum} = \omega_{Lead}</math>

			Moment of inertia is the remaining variable that can tell us the difference in precession angular speed between the two gyroscopes

			Because density is directly proportional to mass and mass is directly proportional to the moment of Inertia, increasing the density would increase the moment of inertia.

			Therefore, the spinning disk made of aluminum would precess faster.



	==Connectedness==		==Connectedness==

Aviphys at 19:50, 23 November 2019

2019-11-23T19:50:18Z

← Older revision		Revision as of 15:50, 23 November 2019
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			'''Claimed by Avirath Dodabele (Fall 2019)'''

	A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.		A [https://en.wikipedia.org/wiki/Gyroscope gyroscope] is a device containing a wheel or disk that is free to rotate about its own axis independent of a change in direction of the axis itself. Since the spinning wheel persists in maintaining its plane of rotation, a [https://www.youtube.com/watch?v=ty9QSiVC2g0 gyroscopic effect] can be observed.

Bbreer6: /* A Mathematical Model */

2019-07-25T17:55:58Z

A Mathematical Model

← Older revision		Revision as of 13:55, 25 July 2019
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	Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:		Thus the only remaining element that is needed to complete the Angular Momentum Principle is the torque. The torque is equal to the distance from the support to the center of mass of the rotor, ''r'', multiplied by the force exerted, which is the mass times gravity. Therefore, since the change in rotational angular momentum is ''LrotΩ'', that must be equal to ''τCM''. By setting the two equations equal to each other, the angular momentum can be isolated to one side. This yields the following result:

	<math>Ω = \frac{~~τCM~~}{L_{rot}} = \frac{rMg}{Iω}</math>		<math>\Omega = \frac{\tau CM}{L_{rot}} = \frac{rMg}{I \omega}</math>

	==Real World Examples==		==Real World Examples==