PX155 - E2 - angular velocity vector

• angular velocity vector $\overrightarrow{\omega }$ has magnitude $\frac{d\theta }{dt}$ and direction parallel to the axis of rotation, sign according to the right hand rule

where, $\overrightarrow{r}$ is a position vector relative to the origin on the axis of rotation

• why?
  • 
  • P moves in a circle of radius $r\sin \theta$, and has velocity $\omega r\sin \theta$ into the page
  • so as claimed, $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
    • use vector cross product