Question

a boy is running along circular track of 15 m diameter. if in 20 seconds he covers half the track, then find his angular speed and linear speed?

Answer 1

The period of a boy motion along circular track $T=2t=40\:\rm s.$

The angular speed

$$\omega=\frac{2\pi}{T}=\frac{2\pi}{40\:\rm s}=\frac{\pi}{20}\:\rm s^{-1}=0.079\:s^{-1}.$$

The linear speed

$$v=\frac{2\pi R}{T}=\frac{2\pi\times 7.5\:\rm m}{40\:\rm s}=\frac{3\pi}{8}\:\rm m/s=1.178\: m/s.$$