Answer
$$
\omega=6.92 \mathrm{rad} / \mathrm{s}
$$
Work Step by Step
$$
\begin{aligned}
& T_S+\Sigma U_{1-2}=T_2 \\
& 0+280\left(\theta_A\right)=\frac{1}{2}\left[800(1.75)^2\right] \omega^2 \\
& \theta_S(2)=\theta_A(0.3) \\
& 5(2 \pi)(2)=\theta_A(0.3) \\
& \theta_A=209.4 \mathrm{rad}
\end{aligned}
$$
Thus
$$
\omega=6.92 \mathrm{rad} / \mathrm{s}
$$
