Answer
$$
39.5 \mathrm{rad} / \mathrm{s}
$$
Work Step by Step
The maximum angular velocity is
$$
\Omega_{n}=\frac{2 \pi \theta_{m}}{T}=\frac{(2 \pi)(\pi \mathrm{rad})}{0.500 \mathrm{s}}=39.5 \mathrm{rad} / \mathrm{s}
$$
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