A flywheel starts from rest and rotates at a constant acceleration of \(2 \mathrm{rad} \mathrm{s}^{-2}\).…
A flywheel starts from rest and rotates at a constant acceleration of \(2 \mathrm{rad} \mathrm{s}^{-2}\). The number of revolutions that it makes in first \(10 \mathrm{~s}\) is
16
24
32
8
Solution
Initial angular velocity of flywheel,
\(\omega_0=0\)
Angular acceleration,
\(\alpha=2 \mathrm{rad} / \mathrm{s}^2\)
Angular displacement in \(t=10 \mathrm{~s}\) is given as
\(\begin{aligned}
\theta & =\omega_0 t+\frac{1}{2} \alpha t^2 \\
& =0 \times 10+\frac{1}{2} \times 2 \times 10^2 \\
& =100 \mathrm{rad}
\end{aligned}\)
\(\begin{aligned}
\text {Number of revolution } & =\frac{\theta}{2 \pi}=\frac{100}{2 \pi}=\frac{100}{2 \times \frac{22}{7}} \\
& =\frac{700}{44}=15.9 \simeq 16
\end{aligned}\)