A particle of mass $m$ is moving in a circle of radius $r$ with a constant angular velocity $\omega$. The torque acting on the particle about the center of the circle is:

Solution

1. Torque is defined as the rate of change of angular momentum, $\tau =\frac{dL}{dt}$.
2. Angular momentum $$\begin{array}{rl}L& =mvr\\ & =m{r}^2\omega \end{array}$$.
3. Since $m$, $r$, and $\omega$ are constant, $L$ is constant.
4. The derivative of a constant is zero.
5. Hence the answer is (C).