Difference between revisions of "Forest UCM Ch3 AngMom"

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: <math>  \left ( \vec \dot r \times \vec p \right )=  \left ( \frac{1}{m} \vec p \times \vec  p \right ) =0 </math> cross product of parallel vectors
 
: <math>  \left ( \vec \dot r \times \vec p \right )=  \left ( \frac{1}{m} \vec p \times \vec  p \right ) =0 </math> cross product of parallel vectors
  
: <math> \left ( \vec r \times \vec \dot p \right )=\left ( \vec r \times \vec F \right )= \vec T</math>
+
: <math> \left ( \vec r \times \vec \dot p \right )=\left ( \vec r \times \vec F \right )= \vec T</math> Definition of Torque
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 +
 
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:<math>\vec{\dot \ell} = \vec T</math>  Newton's second law for angular motion
  
 
=Single particles=
 
=Single particles=

Revision as of 12:29, 14 September 2014

Definition of Angular Momentum

The angular momentum of a single particle is defined as

[math]\vec \ell = \vec r \times \vec p[/math]

Torque

If I take the derivative of angular momentum with respect to time I get

[math]\vec{\dot \ell} = \frac{d}{dt} \left ( \vec r \times \vec p \right )[/math]
[math]= \left ( \vec \dot r \times \vec p \right ) + \left ( \vec r \times \vec \dot p \right )[/math]
[math] \left ( \vec \dot r \times \vec p \right )= \left ( \frac{1}{m} \vec p \times \vec p \right ) =0 [/math] cross product of parallel vectors
[math] \left ( \vec r \times \vec \dot p \right )=\left ( \vec r \times \vec F \right )= \vec T[/math] Definition of Torque


[math]\vec{\dot \ell} = \vec T[/math] Newton's second law for angular motion

Single particles

Kepler's second Law

Forest_UCM_MnAM#Angular_Momentum