Question

A fan is rotating with angular velocity 100 rev s${}^{-1}$. Then it is switched off. It takes $5$ min to stop.
a. Find the total number of revolution made before the fan stops. (assume uniform angular retardation)
b. Find the value of angular retardation.
c. Find the average angular velocity during this interval.

• A. a. $\theta =15000rev.$
  b. $\alpha =\frac{1}{3}rev{s}^{-2}$
  c. $50rev{s}^{-1}$
• B. a. $\theta =16000rev.$
  b. $\alpha =\frac{1}{3}rev{s}^{-2}$
  c. $50rev{s}^{-1}$
• C. a. $\theta =15000rev.$
  b. $\alpha =\frac{1}{2}rev{s}^{-2}$
  c. $50rev{s}^{-1}$
• D. a. $\theta =15200rev.$
  b. $\alpha =\frac{1}{3}rev{s}^{-2}$
  c. $50rev{s}^{-1}$

Answer 1

The correct option is A a. $\theta =15000rev.$

b. $\alpha =\frac{1}{3}rev{s}^{-2}$
c. $50rev{s}^{-1}$
a. $\theta =\left(\frac{\omega +{\omega }_0}{2}\right)t=\left(\frac{100+0}{2}\right)\times 5\times 60=15000rev.$
b. $\omega ={\omega }_0+\alpha t$
$\Rightarrow 0=100-\alpha (5\times 60)\Rightarrow \alpha =\frac{1}{3}rev{s}^{-2}$
c. ${\omega }_{av}=\frac{Totalangleofrotation}{Totaltimetaken}$
$=\frac{15000}{50\times 60}=50rev{s}^{-1}$