Velocity of Point on Rotating Body

Theorem

Let $B$ be a body undergoing rotational motion around an axis $A$.

Let the angular velocity of $B$ about $A$ be $\bsomega$.

Let $O$ be an arbitrary point on $A$.

Let $P$ be a point in $B$ whose position vector with respect to $O$ is $\mathbf r$.

Then the velocity $\mathbf v$ of $P$ is given by:

$\mathbf v = \bsomega \times \mathbf r$

Proof

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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