Predicting the Position of a Rotating System - Revision history

Klsakjsd: Adds Angular Kinematic Equations

2018-12-03T22:17:40Z

Adds Angular Kinematic Equations

← Older revision		Revision as of 18:17, 3 December 2018
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	We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]		We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

			On the other hand, if one utilizes the basic linear Kinematic Equations of [math]x = x_{o} + v_{o} * t + 1/2 * a * t^2[/math], [math]v^2 = v_{o}^2 + a * t[/math], and [math]v = v_{o} + 2 * a * \Delta d[/math], we can adapt these equations for rotational systems.

			The following is the symbol conversion between Linear and Angular Systems.

			{\| class="wikitable"
			\|-
			! Linear
			! Angular
			! Equation
			\|-
			\| [math]x[/math]
			\| [math]\theta[/math]
			\| [math]\theta = \frac{x}{r}[/math]
			\|-
			\| [math]v[/math]
			\| [math]\omega[/math]
			\| [math]\omega = \frac{v}{r}[/math]
			\|-
			\| [math]a[/math]
			\| [math]\alpha[/math]
			\| [math]\alpha = \frac{a}{r}[/math]
			\|-
			\| [math]f[/math]
			\| [math]\tau[/math]
			\| [math]\tau = f \times r[/math]
			\|}

			In other words, the angular systems versions of kinematic equations are:

			[math]\theta = \theta_{o} + \omega_{o} * t + \frac{1}{2} * \alpha * t^2[/math]

			[math]\omega = \omega_{o} + \alpha * t[/math]

			[math]\omega^2 = \omega_{o}^2 + 2 * \alpha * \Delta \theta[/math]

			Simply plug in known values, in radians, and solve for the unknown. Just like the linear kinematic equations.

	===A Computational Model===		===A Computational Model===

Awhitacre7 at 03:52, 6 December 2015

2015-12-06T03:52:52Z

← Older revision		Revision as of 23:52, 5 December 2015
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	==The Main Idea==		==The Main Idea==
	The position of a rotating system can be predicted by predicting the angle over which the object will rotate ~~though~~ out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.		The position of a rotating system can be predicted by predicting the angle over which the object will rotate through out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

	===A Mathematical Model===		===A Mathematical Model===

Awhitacre7: /* External links */

2015-12-05T22:39:44Z

External links

← Older revision		Revision as of 18:39, 5 December 2015
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	===External links===		===External links===
	[https://www.youtube.com/watch?v=0k276y9kuQQ Angular Momentum - Science Theater Video ]		[https://www.youtube.com/watch?v=0k276y9kuQQ Angular Momentum - Science Theater Video ]

	[http://chaos.utexas.edu/wp-uploads/2012/03/Lecture_24_post.pdf A Guide to the Angular Momentum Principle]		[http://chaos.utexas.edu/wp-uploads/2012/03/Lecture_24_post.pdf A Guide to the Angular Momentum Principle]

Awhitacre7: /* External links */

2015-12-05T22:39:24Z

External links

← Older revision		Revision as of 18:39, 5 December 2015
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	===External links===		===External links===
			[https://www.youtube.com/watch?v=0k276y9kuQQ Angular Momentum - Science Theater Video ]
	~~Internet resources on this topic~~		[http://chaos.utexas.edu/wp-uploads/2012/03/Lecture_24_post.pdf A Guide to the Angular Momentum Principle]

	==References==		==References==

Awhitacre7 at 22:33, 5 December 2015

2015-12-05T22:33:54Z

← Older revision		Revision as of 18:33, 5 December 2015
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	[[File:Rotating_Sphere.gif\|thumb\|right\|300px\|Visual of a rotating system.]]		[[File:Rotating_Sphere.gif\|thumb\|right\|300px\|Visual of a rotating system.]]
	In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of ~~the~~ system.		In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of a rotating system.

	==The Main Idea==		==The Main Idea==

Awhitacre7 at 22:33, 5 December 2015

2015-12-05T22:33:19Z

← Older revision		Revision as of 18:33, 5 December 2015
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	~~''(claimed by Anna Marie Whitacre, awhitacre7)''~~
	[[File:Rotating_Sphere.gif\|thumb\|right\|300px\|Visual of a rotating system.]]		[[File:Rotating_Sphere.gif\|thumb\|right\|300px\|Visual of a rotating system.]]
	In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.		In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.
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	===A Computational Model===		===A Computational Model===
			The position of a rotating system can be predicted using the following vPython code below. [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. Take note that the default values in the code computationally calculate the answers to [[#Middling\|this physics problem]].
			[[File:Pythonscreenshot.png\|center\|550px\|vPython code for solving rotational position.]]

	The position of a rotating system can be predicted using the following vPython code [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. The default values in the code computationally calculate the answers to [[#Middling\|this physics problem]].

	==Examples==		==Examples==

Awhitacre7 at 22:25, 5 December 2015

2015-12-05T22:25:26Z

← Older revision		Revision as of 18:25, 5 December 2015
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	===A Computational Model===		===A Computational Model===

	The position of a rotating system can be predicted using the following vPython code [https://trinket.io/python/22d3018e32]. The default values in the code computationally calculate the answers to [[#Middling\|this physics problem]].		The position of a rotating system can be predicted using the following vPython code [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. The default values in the code computationally calculate the answers to [[#Middling\|this physics problem]].

	==Examples==		==Examples==

Awhitacre7 at 22:20, 5 December 2015

2015-12-05T22:20:01Z

← Older revision		Revision as of 18:20, 5 December 2015
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	===A Computational Model===		===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~~]		The position of a rotating system can be predicted using the following vPython code [https://trinket.io/python/22d3018e32]. The default values in the code computationally calculate the answers to [[#Middling\|this physics problem]].

	==Examples==		==Examples==

Awhitacre7: /* Middling */

2015-12-05T21:49:45Z

Middling

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	[[File:Mida.jpg\|400px\|center\|]]		[[File:Mida.jpg\|400px\|center\|]]
	'''(b)''' What is the average angular speed?		'''(b)''' What is the average angular speed?
			[[File:Midb.jpg\|400px\|center\|]]
	'''(c)''' Through how big an angle did the wheel turn?		'''(c)''' Through how big an angle did the wheel turn?
			[[File:Midc.jpg\|400px\|center\|]]
	'''(d)''' How much string came off the wheel?		'''(d)''' How much string came off the wheel?
			[[File:Midd.jpg\|400px\|center\|]]

	==Connectedness==		==Connectedness==

Awhitacre7 at 21:45, 5 December 2015

2015-12-05T21:45:36Z

← Older revision		Revision as of 17:45, 5 December 2015
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	'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?		'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
			[[File:Simplea.jpg\|400px\|center\|]]

	'''(b)''' How far did your hand move during this time interval?		'''(b)''' How far did your hand move during this time interval?
			[[File:Easbi.jpg\|400px\|center\|]]

			[[File:Easbii.jpg\|400px\|center\|]]
	===Middling===		===Middling===
	A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.		A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

	'''(a)''' What is the final angular speed?		'''(a)''' What is the final angular speed?
			[[File:Mida.jpg\|400px\|center\|]]
	'''(b)''' What is the average angular speed?		'''(b)''' What is the average angular speed?