Question

Particle $P$ shown in figure is moving in a circle of radius $R=10cm$ with linear speed $v=2m/s$. Find the angular speed of particle about point $O$

• A. $10\text{rad/s}$
• B. $20\text{rad/s}$
• C. $30\text{rad/s}$
• D. $40\text{rad/s}$

Answer 1

The correct option is A $10\text{rad/s}$



Angular velocity of particle wrt centre $C$
${\omega }_c=\frac{v_{\perp }}{R}=\frac{v}{R}=\frac{2}{0.1}$
${\omega }_c=20\text{rad/s}$





from above figure at any position $P$, if the particle subtends an angle $\theta$ at $O$, corresponding angle at $C$ is $2\theta$

So, Angular velocity of particle wrt centre $C$
${\omega }_c=\frac{d}{dt}\left(2\theta \right)=2\frac{d\theta }{dt}$

Angular velocity of $P$ about $O$ is
${\omega }_0=\frac{d\theta }{dt}=\frac{{\omega }_c}{2}$
${\omega }_0=10\text{rad/s}$