Difference between revisions of "Forest UCM Ch3 AngMom"

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:<math>\vec{\dot \ell} = \frac{d}{dt} \left ( \vec r \times \vec p \right )</math>
 
:<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 ( \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 \cal T</math>
  
 
=Single particles=
 
=Single particles=

Revision as of 12:26, 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 \cal T[/math]

Single particles

Kepler's second Law

Forest_UCM_MnAM#Angular_Momentum