A body is in pure rotation. linear speed v of a particle, distance r of particle from axis and a

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3-2.Motion in Plane

medium

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

$\omega \propto \frac{1}{r}$

$\omega \propto r$

$\omega = 0$

$\omega $ is independent of $r$

Solution

Explanation $\Rightarrow$ In the given Relation,

$\omega=v / r$

$\omega$ is the Constant of Proportionality, $v$ is the Velocity of the Particles which is directly proportional to the distance of the particles from the axis $(r).$

$\therefore v \propto r$

$\Rightarrow v=\omega \times r$

since, $\omega$ is the constant of Proportionality, its value will be remains same for the given values of $v$ and $r .$

$\therefore$ Option $(d)$. is correct.

Standard 11

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

Solution

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