Question

A fan is rotating with angular velocity 100 revs/sec. Then it is switched off. It takes 5 minutes to stop.
(i) Find the total number of revolutions made before it stops. (Assume uniform angular retardation)
(ii) Find the value of angular retardation.
(iii) Find the average angular velocity during this interval.

• A. (i) $15000revs$
  (ii) $\frac{1}{3}rev/s^2$
  (iii) $50revs/s$
• B. (i) $1500revs$
  (ii) $\frac{1}{2}rev/s^2$
  (iii) $50revs/s$
• C. (i) $10000revs$
  (ii) $\frac{1}{2}rev/s^2$
  (iii) $50revs/s$
• D. (i) $12000revs$
  (ii) $\frac{1}{6}rev/s^2$
  (iii) $75revs/s$

Answer 1

The correct option is A

(i) $15000revs$
(ii) $\frac{1}{3}rev/s^2$
(iii) $50revs/s$

Let $\alpha$ be the angular retardation.
Now, $\omega ={\omega }_0-\alpha t\Rightarrow 0=100\times 2\pi -\alpha (5\times 60)\Rightarrow \alpha =\frac{2\pi }{3}rad/s^2=\frac{1}{3}revs/s^2$
From third equation, ${\omega }^2={\omega }_0^2-2\alpha \theta$
Substituting values we get, $\theta =30000\pi$
Hence, number of revolutions, $n=\frac{30000\pi }{2\pi }=15000$
Now, ${\omega }_{av}\times t=\theta {\omega }_{av}=\frac{30000\pi }{5\times 60}=100\pi rad/s=50revs/s$