A flywheel slows down uniformly from $1200 \mathrm{rpm}$ to $600 \mathrm{rpm}$ in $5 \mathrm{~s}$. Find the number of revolutions made by the wheel in $5 \mathrm{~s}$.
Q 32.13
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Data : $\omega_0=1200 \mathrm{rpm}, \omega=600 \mathrm{rpm}, \mathrm{f}=5 \mathrm{~s}$
Since the flywheel slows down uniformly, its angular acceleration is constant. Then, its average angular speed,
$
\begin{aligned}
& \omega_{\mathrm{av}}=\frac{\omega_{\mathrm{o}}+\omega}{2}=\frac{1200+600}{2} \\
& =900 \mathrm{rpm}=\frac{900 \mathrm{rev}}{60 \mathrm{~s}}=15 \mathrm{rps}
\end{aligned}
$
Its angular displacement in time $t$,
$\theta=\omega_{\text {av }} \cdot \mathrm{t}=15 \times 5=75$ revolutions
Since the flywheel slows down uniformly, its angular acceleration is constant. Then, its average angular speed,
$
\begin{aligned}
& \omega_{\mathrm{av}}=\frac{\omega_{\mathrm{o}}+\omega}{2}=\frac{1200+600}{2} \\
& =900 \mathrm{rpm}=\frac{900 \mathrm{rev}}{60 \mathrm{~s}}=15 \mathrm{rps}
\end{aligned}
$
Its angular displacement in time $t$,
$\theta=\omega_{\text {av }} \cdot \mathrm{t}=15 \times 5=75$ revolutions
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