Question

A circular disc is rotating with constant angular velocity about an axis that passes through the center. A particle '$ P$' is kept at a distance of $ 2m$ from the center and another particle '$ Q$' at a distance of $ 3m$ from the center. Which of these will have higher centripetal acceleration?

Answer 1

Step 1: Given data

Distance of particle $P$ from center($R_P$) =$2m$

Distance of particle $Q$ from center($R_Q$) =$3m$

Let that particle rotate in a circular motion with constant angular velocity $\omega$

Step 2: Applied formulae

The centripetal acceleration is given by :$\alpha ={\omega }^{2}R$

Since $\omega$ is constant, acceleration depends on $R$

$R$ is the distance from the center

We know, $R_Q$ is greater than $R_P$

${\omega }^2{R}_{Q_{}}>{\omega }^2{R}_P$

Therefore particle $Q$ will have greater centripetal acceleration.