Topic: Engineering Mathematics
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: The velocity vector of a point on the rigid body is given by $\vec{v}=\vec{\omega}\times\vec{r}$. Taking the curl of the velocity field yields $\nabla\times\vec{v}=\nabla\times(\vec{\omega}\times\vec{r})$. Since the angular velocity $\vec{\omega}$ is constant, this resolves to $2\vec{\omega}$, making the magnitude $2\omega$.