Question

A fan is rotating with angular velocity $100 \mathrm{rev} / \mathrm{sec}$. Then it is switched off. It takes 5 minutes to stop.

(a) Find the total number of revolution made before it stops (Assume uniform angular retardation).

(b) Find the value of angular retardation.

(c) Find the average angular velocity during this interval.

Answer 1

(a) $\theta=\left(\frac{\omega+\omega_{0}}{2}\right) \mathrm{t}=\left(\frac{100+0}{2}\right) \times 5 \times 60$

$=15000$revolution.

(b) $\omega=\omega_{0}+\alpha t \Rightarrow 0=100-\alpha(5 \times 60)$

$\Rightarrow$ $\alpha=\frac{1}{3} \mathrm{rev} . / \mathrm{sec}^{2}$

(c) $\omega_{\mathrm{av}}=\frac{\text { Total Angle of Rotation }}{\text { Total time taken }}=\frac{15000}{50 \times 60}=50 \mathrm{rev} . / \mathrm{sec}$.