Answer
$$ \omega_p=1.19 \mathrm{rad} / \mathrm{s}
$$
Work Step by Step
$$
\begin{aligned}
& \Sigma M_s=I_z \Omega_y w_z \\
& 8(0.5)=\left[\frac{1}{2}\left(\frac{8}{32.2}\right)(0.3)^2\right] w_p(300) \\
& \omega_p=1.19 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
