Question

A fan is revolving with an angular speed of $120\text{rpm}$. Suddenly a boy switches off the fan and it eventually comes to rest by making 30 revolutions in 2 mins. The average angular velocity of the fan is

• A. $\pi \frac{\text{rad}}{\text{s}}$
• B. $2\pi \frac{\text{rad}}{\text{s}}$
• C. $\frac{\pi }{2}\frac{\text{rad}}{\text{s}}$
• D. $4\pi \frac{\text{rad}}{\text{s}}$

Answer 1

The correct option is C $\frac{\pi }{2}\frac{\text{rad}}{\text{s}}$

Angular displacement of fan $\Delta \theta =30\times 2\pi =60\pi$
Time elapsed before fan comes to rest $\Delta t=2\text{mins}=120\text{s}$

${\omega }_{\text{avg}}=\frac{\Delta \theta }{\Delta t}=\frac{30\times 2\pi }{120}=\frac{\pi }{2}\text{rad/s}$