Question

A body is in pure rotation. The linear speed $v$ of a particle, the distance $r$ of a 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. $\omega =0$
• D. $\omega$ is independent of $r$

Answer 1

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

In the given Relation,

$\omega =v/r$

v =velocity of the particle which is directly proportional to distance of particle from thew axis.

$\omega$ is constant of proportionality and its value will remain same.In case of pure rotation all particle of the rigid body will have same angular velocity.

Also,

v is directly proportional to r.

v=$\omega$*r