Question

A wheel is rotating at $1800 \,rpm$ about its own axis. When the power is switched off, it comes to rest in $2$ minutes. Then the angular retardation in $rad\,s^{-2}$ is

• A. $2 \pi$
• B. $ \pi$
• C. $\frac{\pi}{2}$
• D. $\frac{\pi}{4}$
• E. $\frac{\pi}{6}$

Answer 1

Answer: (C)

First equation of rotational motion
$\omega=\omega_{0}+\alpha t$
where $\omega =2 \pi n=2 \pi \times \frac{1800}{60} $
$=60 \pi\, rps $
$\omega_{0} =0$
$t =2 \times 60=120\, s$
$60 \pi =0+\alpha \times 120$
$\alpha =\frac{60 \pi}{120} $
$\alpha =\frac{\pi}{2} \,rad / s ^{2}$