Question

A fan is rotating with angular velocity $100\text{rev/sec}$. Then, it is switched off. It takes $5$ minutes to stop. Find the average angular velocity during this interval.
(correct answer + 1, wrong answer - 0.25)

• A. $100\text{rev/sec}$
• B. $75\text{rev/sec}$
• C. $125\text{rev/sec}$
• D. $50\text{rev/sec}$

Answer 1

The correct option is D $50\text{rev/sec}$

Given, initial angular velocity, ${\omega }_0=100\text{rev/s}$
Final angular velocity, $\omega =0\text{rev/s}$
$\therefore$ Total number of revolution made by the fan, $\theta =\left(\frac{\omega +{\omega }_0}{2}\right)t$
$=\frac{0+100}{2}\times 5\times 60=15000\text{rev}$
$\therefore$ Average angular velocity in this interval $=\frac{15000}{5\times 60}=50\text{rev/sec}$