Question

A wheel is rotating at $900$ r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian $/ s ^2$ is $\frac{\pi}{x}$. Find the value of $x$.

Answer 1

$\omega_{ i }=\frac{900}{60} \times 2 \pi=30 \pi rad / s , \omega_{ f }=0, t =60 \,s$
$\omega_{ f }=\omega_{ i }+\alpha t $
$\therefore \alpha=\frac{\omega_{ f }-\omega_{ i }}{ t }=\frac{0-30 \pi}{60}=-\frac{\pi}{2} rad / s ^2$
Here, -ve sign shows angular retardation.