A body is in pure rotation. The linear speed | vedclass

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Question

(D) In pure rotation,all particles of a rigid body rotate with the same angular velocity $\omega$ about the axis of rotation.The relation is given by

Vedclass · Accepted Answer

$\omega$ is independent of $r$

Vedclass · Answer

(D) In pure rotation,all particles of a rigid body rotate with the same angular velocity $\omega$ about the axis of rotation.The relation is given by $v = \omega r$,which implies $\omega = \frac{v}{r}$.For a rigid body undergoing pure rotation,the angular velocity $\omega$ is a property of the entire body and is constant for all particles at any given instant,regardless of their distance $r$ from the axis.As the distance $r$ increases,the linear speed $v$ increases proportionally such that the ratio $\frac{v}{r}$ remains constant.Therefore,$\omega$ is independent of $r$.Thus,option $(d)$ is correct.

$A$ body is in pure rotation. The linear speed $v$ of a particle,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,

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