Question:
A wheel of moment of inertia $0.500 \mathrm{~kg}_{-} \mathrm{m}^{2}$ and radius $20.0 \mathrm{~cm}$ is rotating about its axis at an angular speed of $20.0 \mathrm{rad} / \mathrm{s}$. It picks up a stationary particle of mass $200 \mathrm{~g}$ at its edge. Find the new angular speed of the wheel.
Solution:
Since, $\tau_{\text {ext }}=0$
$\therefore L_{i}=L_{f}$
$I_{i} \omega_{i}=I_{f} \omega_{f}$
$(0.5)(20)=\left[0.5+(0.2)^{(0.5)^{2} \omega_{f}}\right]$
$\omega_{f}=19.7 \frac{\text { rad }}{\sec }$
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