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.
• C. ω_av = 100π rad/s
• D. ω_av = 10 π rad/s

Answer 1

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

The correct options are
A

No. of revolutions = 15000

B

C

ω_av = 100π 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)

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