Question

A wheel is rotating at $1800rpm$ about its own axis. When the power is switched oft it comes to rest in $2$ min. Then, the angular retardation in rad $s^{-1}$ is

• A. $2\pi$
• B. $\pi$
• C. $\pi /2$
• D. $\pi /4$
• E. $\pi /6$

Answer 1

Answer: (C)

$\pi /2$

First equation of rotational motion
$\omega ={\omega }_0+\alpha t$
where $\omega =2\pi n=2\pi \times \frac{1800}{60}$
$=60\pi rps$
${\omega }_0=0$
$t=2\times 60=120s$
$60\pi =0+\alpha \times 120$
$\alpha =\frac{60\pi }{120}$
$\alpha =\frac{\pi }{2}rad/s^2$