Answer
$$\omega=19.8 \mathrm{rad} / \mathrm{s}
$$
Work Step by Step
$$
\nu_G=0.4 \omega
$$
Datum at lowest point.
$$
\begin{aligned}
& T_1+V_1=T_2+V_2 \\
& 0+7(9.81)(5)=\frac{1}{2}(7)(0.4 \omega)^2+\frac{1}{2}\left[7(0.3)^2\right] \omega^2+0 \\
& \omega=19.8 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
