Question

A wheel is rotating at $900r.p.m,$ about its axis. When power is cut off it comes to rest in $1minute$. The angular retardation in $rad/s^2$ is:

• A. $\pi /2$
• B. $\pi /4$
• C. $\pi /6$
• D. $\pi /8$

Answer 1

The correct option is A $\pi /2$

Initially $\nu =900r.p.m=\frac{900}{60}=15s^{-1}$

Thus ${\omega }_1=2\pi \nu =30\pi rad/s$ and ${\omega }_2=0$

Using, ${\omega }_2={\omega }_1+\alpha t$, where $t=60s$, we get:

$0=30\pi +\alpha \left(60\right)$

or, $\alpha =-\frac{\pi }{2}rad/s^2$ (-ve sign shows angular retarding acceleration)