Question

A particle moves uniformly in a circle of radius $25cm$ at two revolution per second. Find the acceleration of the particle in $m/s^2$.

Answer 1

Given: Radius $=25cm=\frac{1}{4}m$

$2revolution/sec=\omega =\frac{2\times 2\pi }{1}=4\pi rad/sec$ ($1$revolution $=2\pi rad$)

Centripetal Acceleration $={\omega }^{2}r=(4\pi {)}^2\times \frac{1}{4}=4{\pi }^{2}m/s^2$

Tangential acceleration$=0$ (As $\omega$ is constant which means $v$ is constant in magnitude)

$\therefore$ Total $a=4{\pi }^{2}m/s^2$