Topic: Engineering Mechanics
A rigid body is rotating with constant angular velocity $\omega$ about a fixed axis, if V is the velocity of a point of the body, then curl $V=$
- A. $\omega$
- B. $\omega^{2}$
- C. $2\omega$
- D. $2\omega^{2}$
Answer: C. $2\omega$
Explanation: We know that angular velocity $\omega = \frac{1}{2}|\nabla\times V|$. Therefore, $2\omega = |\nabla\times V|$. Since curl $V = \nabla\times V$, the curl of the velocity field for a rotating rigid body is $2\omega$.