Question

A fan is rotating with an angular speed of $150\pi$ rad/s. After switching it off, it takes $10$ minutes to stop. Find the total number of revolutions made before the fan stops. (Assume constant angular retardation)

• A. $45000\pi$
• B. $22500\pi$
• C. $50000\pi$
• D. $22500$

Answer 1

The correct option is D $22500$

We know, $w_0=150\pi \text{rad/s}$
$t=10$ minutes = $10\times 60\text{s}$
$t=600\text{s}$
we know, $w=w_0+\alpha t$
$0=150\pi +\alpha \times 600$
$\alpha =-\frac{\pi }{4}\text{r}ad/s^2$
Using, $w^2-w_0^2=2\alpha \theta$
$0^2-(150\pi {)}^2=2\times (-\frac{\pi }{4})\theta$
$\theta =45000\pi$ radian
Angle covered is one revolution $=2\pi$
Number of revolutions = $\frac{\text{total angle covered}}{\text{angle covered in one revolution}}$
$=\frac{45000\pi }{2\pi }$
$=22500$