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 $P$ with respect to $O$ as a function of time.

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

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 $P$ with respect to $O$.

Dimension

Angular velocity has dimension $\mathsf T^{-1}$.

Units

The unit of measurement of angular velocity is the radian per second.

Symbol

The usual symbol used to denote angular velocity is $\bsomega$.

Also see

• Results about angular velocity can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angular velocity
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angular velocity
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): angular velocity