Definition:Angular Velocity
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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