Question

a stone attached to the end of an inelastic string is whirled round in a circular path of radius 30cm if the stone makes 9 complete revolutions in 3 seconds, calculate its angular and linear velocities.

Answer 1

The period of revolution of the stone

$$T=\frac{t}{N}=\frac{3\:\rm s}{9}=\frac{1}{3}\:\rm s$$

The angular velocity of the stone

$$\omega=\frac{2\pi}{T}=\frac{2\pi}{1/3\:\rm s}=6\pi\:\rm s^{-1}=18.84\:\rm s^{-1}$$

The linear velocity of the stone

$$v=\omega R=6\pi\:\rm s^{-1}\times 0.3\:\rm m=5.652\: \rm m/s$$