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 \mathcal T[/math] Definition of Torque
- [math]\vec \mathcal T =\vec{\dot \ell} [/math] Newton's second law for angular motion
Kepler's second Law
Forest_UCM_MnAM#Angular_Momentum