Angular Momentum
The angular momentum of a mass rotating in a circle of
radius
with angular velocity
(rad/s), is defined by
![$\displaystyle L \eqsp I\omega
$](http://www.dsprelated.com/josimages_new/pasp/img2850.png)
![$ I=mR^2$](http://www.dsprelated.com/josimages_new/pasp/img2719.png)
Relation of Angular to Linear Momentum
Recall (§B.3) that the momentum of a mass traveling
with velocity
in a straight line is given by
![$\displaystyle p = m v,
$](http://www.dsprelated.com/josimages_new/pasp/img2683.png)
![$ m$](http://www.dsprelated.com/josimages_new/pasp/img6.png)
![$ R$](http://www.dsprelated.com/josimages_new/pasp/img9.png)
![$ \omega $](http://www.dsprelated.com/josimages_new/pasp/img15.png)
![$\displaystyle L \eqsp I\omega,
$](http://www.dsprelated.com/josimages_new/pasp/img2851.png)
![$ I=mR^2$](http://www.dsprelated.com/josimages_new/pasp/img2719.png)
![$ R$](http://www.dsprelated.com/josimages_new/pasp/img9.png)
![$\displaystyle v \eqsp R\omega.
$](http://www.dsprelated.com/josimages_new/pasp/img2852.png)
![$ I$](http://www.dsprelated.com/josimages_new/pasp/img238.png)
![$ v$](http://www.dsprelated.com/josimages_new/pasp/img345.png)
Thus, the angular momentum
![$ L$](http://www.dsprelated.com/josimages_new/pasp/img335.png)
![$ R$](http://www.dsprelated.com/josimages_new/pasp/img9.png)
![$ p=mv$](http://www.dsprelated.com/josimages_new/pasp/img2793.png)
Linear momentum can be viewed as a renormalized special case of angular momentum in which the radius of rotation goes to infinity.
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Angular Momentum Vector
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Vector Cross Product