Answer
$$
v_c=31.9 \mathrm{~m} / \mathrm{s}
$$
Work Step by Step
$$
\begin{aligned}
T_1+V_1 & =T_2+V_2 \\
0+0 & =\frac{1}{2}\left[\frac{1}{12}\left(\frac{180}{32.2}\right)(8)^2\right] \omega^2+\frac{1}{2}\left(\frac{180}{32.2}\right)(1 \omega)^2-180(4) \\
\omega & =6.3776 \mathrm{rad} / \mathrm{s} \\
v_c & =\omega(5)=6.3776(5)=31.9 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
