A flywheel is rotating at a rate of $150 \mathrm{rev} / \mathrm{minute}$. If it slows at constant…
A flywheel is rotating at a rate of $150 \mathrm{rev} / \mathrm{minute}$. If it slows at constant retardation of $\pi \mathrm{rads}^{-2}$, then the time required for the wheel to come to rest is
$2.5 \mathrm{~s}$
$5 \mathrm{~s}$
$4 \mathrm{~s}$
$6 \mathrm{~s}$
Solution
Angular velocity of flywheel, $\omega=150$
$\mathrm{rev} /$ minute $=\frac{150 \times 2 \pi}{60}$
$=5 \pi \mathrm{Rad} / \mathrm{s}$
Angular acceleration, $\alpha=\pi \mathrm{rad} / \mathrm{s}^2$
$\omega=\omega_0+\alpha t$
The time required far the wheel to come to rest is
$\mathrm{t}=\frac{\omega-\omega_0}{\alpha}=\frac{5 \pi-0}{\pi}=5 \mathrm{~s}$