Question

A body is in pure rotation. The linear speed $v$ of the particle on the body, the distance $r$ of the particle from the axis and the angular velocity $\omega$ of the body are related as $\omega =\frac{v}{r}$. Thus

• A. $\omega \propto \frac{1}{r}$
• B. $\omega \propto r$
• C. $v$
• D. $\omega$ is independent of $r$

Answer 1

The correct option is D $\omega$ is independent of $r$

In a pure rotation, angular velocity of all the particles remains same and does not depend on the position of the particle from the axis of rotation.

$v\propto r$ and $\omega$ is the constant of proportionality. Thus $v=\omega r$.

So $\omega$ is independent of $r$.

Hence option D is the correct answer.