Question

A piece of stone of mass 0.2 kg is tied to the end of a string 1 m long and whirled in a horizontal circle about other end of the string. If it performs 90 revolutions per minute, Calculate
a) angular velocity
b) Centripetal acceleration
c) centripetal force and
d) tension in string.

Answer 1

Mass, $m=0.2$ $kg$

Radius, $r=1$ $m$

Angular speed, $\omega =90$ $rpm$

$⟹\omega =\frac{90}{60}$

$⟹\omega =1.5$ $rps$

$⟹\omega =3\pi$ $rad/s$

$\left(a\right)$ Angular velocity, $\omega =3\pi$ $rad/s$

$\left(b\right)$ Centripetal acceleration. $a=r{w}^2$

$⟹a=1\times 3\pi \times 3\pi$

$⟹a=9{\pi }^2$ $m/s^2$

$\left(c\right)$ Centripetal Force, $F=ma$

$⟹F=0.2\times 9{\pi }^2$

$⟹F=1.8{\pi }^2$ $N$

$\left(d\right)$ Tension in string, $=$ Centripetal Force

$⟹T=F=1.8{\pi }^2$ $N$