Forest UCM Ch3 AngMom - Revision history

Foretony: /* Moment of Inertia of a Uniform disk */

2014-09-15T01:14:04Z

Moment of Inertia of a Uniform disk

2014-09-15T01:08:26Z

Moment of Inertia of a Univerom disk

2014-09-15T01:07:04Z

Definiitons

2014-09-14T23:00:28Z

Examples

2014-09-14T23:00:19Z

Moment of Inertia

2014-09-14T22:54:28Z

Definiitons

2014-09-14T22:52:33Z

Definiitons

2014-09-14T22:51:38Z

Moment of Inertia

2014-09-14T16:48:10Z

Conservation of Angular Momentum

2014-09-14T16:10:27Z

Moment of Inertia

@@ Line 153: / Line 153: @@
 ==Moment of Inertia of a Uniform disk==
-Find the center of mass for a disk of radius <math>R</math> and area mass density <math>\rho=m/A</math>
+Find the center of mass for a disk of radius <math>R</math> and area mass density <math>\sigma=m/A</math>
-:<math>x_{cm} = \frac{1}{m} \int x \sigma dA = \frac{1}{m} \int x \rho r dr d\theta</math>
+:<math>I = \int \sigma r^2 dA = \int \sigma r^2 r dr d\theta</math>
-::<math>= \frac{\rho}{m}\int r \cos \theta r dr d\theta</math>
+::<math>= \sigma \int_0^R r^3 dr \int_0^{2\pi} d\theta </math>
-::<math>= \frac{1}{A}\int  r^2 dr \int d(\sin \theta)</math>
+::<math>= \sigma \int_0^R r^3 dr (2 \pi)</math>
-::<math>= \frac{1}{A}\int  r^2 dr \left . \sin \theta \right |_0^{2\phi}</math>
+::<math>= 2\pi \sigma \frac{R^4}{4} </math>
-::<math>= \frac{1}{A}\int  r^2 dr \left . \sin \theta \right |_0^{2\phi}</math>
+::<math>=\frac{1}{2} \frac{M}{\pi R^2}  R^4</math>
-::<math>= \frac{1}{A}\int  r^2 dr (0) = 0</math>
+::<math>=\frac{1}{2} M R^2</math>
 [[Forest_UCM_MnAM#Angular_Momentum]]

@@ Line 151: / Line 151: @@
 :<math>I = \int \rho r^2 dV</math>
-==Moment of Inertia of a Univerom disk==
+==Moment of Inertia of a Uniform disk==
 [[Forest_UCM_MnAM#Angular_Momentum]]

@@ Line 151: / Line 151: @@
 :<math>I = \int \rho r^2 dV</math>
+==Moment of Inertia of a Univerom disk==
 [[Forest_UCM_MnAM#Angular_Momentum]]

@@ Line 151: / Line 151: @@
 :<math>I = \int \rho r^2 dV</math>
-=Examples=
 [[Forest_UCM_MnAM#Angular_Momentum]]

← Older revision		Revision as of 23:00, 14 September 2014
Line 150:		Line 150:

	:<math>I = \int \rho r^2 dV</math>		:<math>I = \int \rho r^2 dV</math>
		+
		+	=Examples=
		+
		+

	[[Forest_UCM_MnAM#Angular_Momentum]]		[[Forest_UCM_MnAM#Angular_Momentum]]

@@ Line 143: / Line 143: @@
 ==Definiitons==
-;system of particles
+;for a system of particles
 :<math>I = \sum_i^N m_i r_i^2</math>
-;Rigid Bodies
+;for a Rigid Bodies
 :<math>I = \int \rho r^2 dV</math>
 [[Forest_UCM_MnAM#Angular_Momentum]]

← Older revision		Revision as of 22:51, 14 September 2014
Line 141:		Line 141:
	=Moment of Inertia=		=Moment of Inertia=

		+	==Definiitons==
		+
		+	;system of particles
		+
		+	:<math>I = \sum_i^N m_i r_i^2</math>
		+
		+	;Rigid Bodies
		+
		+	:<math>I = \int m r^2 dr</math>

	[[Forest_UCM_MnAM#Angular_Momentum]]		[[Forest_UCM_MnAM#Angular_Momentum]]

@@ Line 134: / Line 134: @@
-;If the NET external torque on a system of particles is zero
+;If
-;Then the angular momentum is constant
+:the NET external torque on a system of particles is zero
 =Moment of Inertia=
 [[Forest_UCM_MnAM#Angular_Momentum]]