Definition:Angular Velocity

Definition
Let $P$ be a particle moving in the plane.

Let $O$ be a distinguished point in the plane.

Let $\map {\mathbf r} t$ be the position vector of $P$ $O$ as a function of time.

Let $\map {\mathbf v} t$ be the velocity of $P$ $O$ as a function of time.


 * Angular-Velocity.png

Let $\mathbf v_\perp$ denote the component of $\mathbf v$ perpendicular to the position vector $\mathbf r$.

This vector $\mathbf v_\perp$ is known as the angular velocity of $P$ $O$.