# About an example related to angular momentum in a textbook

1. Mar 10, 2012

First let's agree on the symbols lets call angular velocity: $\omega = \frac{rxv}{||r||^2}$ , angular momentum $L=rxmv$ and Lineal Momentum:$P=mv$. Being that defined, the book attemps to proof that $L$ and $\omega$ have generally different directions, here is the first problem i encountered, for what i know $m||r||^2\omega = L$ being $m||r||^2$ That means that Angular Velocity and Angular Momentum are parallel therefore have the same direction, the example proceed as following: 2 puntual mass are united by a rigid bar of despicable mass, therefore both have the same angular momentum. the momentum of body 1 is $L_1 = r_1xm_1v_1$ and it explicitly say that it's easy to see that it's contained in the plane given by $P_1 P_2 \omega$ (which i fail to see) being the direction perpendiculat to the line that unites $P_1$ with $P_2$ and that $L_2$ Has the same direction that $L_1$. Therefore the Angular Impulse make an angle of $\frac{\pi}{2}-\alpha$ with the axis of rotation($\omega$). Well that'd be an example i'd really appreciate if someone can clarify my doubts, i don't have a teacher to ask since i study by my own.