Question

A fan is rotating with angular velocity 100 $\frac{rev}{sec}$. Then it is switched off. It takes 5 minutes to stop. (i) Find the total number of revolution 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. No. of revolutions = 15000
• B. $\alpha$ = $\frac{-2}{3}\pi \frac{rad}{s^2}$
• C. ${\omega }_{av}$ = $100\pi$ $\frac{rad}{s}$
• D. ${\omega }_{av}$ = $10\pi$ $\frac{rad}{s}$

Answer 1

Answer: (A), (B), (C)

${\omega }_{av}$ = $100\pi$ $\frac{rad}{s}$

${\omega }_0=\frac{\Delta \theta }{\Delta t}=100\times 2\pi =200\pi$

t = 5 min = 5 x 60 = 300s

$\omega ={\omega }_0+\alpha t$

⇒ 0 = 100 x 2π + α (300)

$\Rightarrow \alpha =-\frac{200\pi }{300}=\frac{-2\pi }{3}rad/s^2...............................\left(ii\right)$

$\therefore \theta ={\omega }_{0}t+\frac{1}{2}\left(\frac{-2}{3}\pi \right)\left({300}^2\right)$

= 60,000π $-\frac{\pi }{3}\times$ 90,000

= 60,000π – 30,000π

⇒ 30,000π radians

No. of revolution = $\frac{\theta }{2\pi }=\frac{30000\pi }{2\pi }$ = 15,000 rev ................................(i)

${\omega }_{av}=\frac{\theta }{t}=\frac{30,000\pi }{300}=100\pi \frac{rad}{s}......................\left(iii\right)$