Answer
$$\omega=1.80 \mathrm{rad} / \mathrm{s}
$$
Work Step by Step
$$
\begin{aligned}
& T_1+V_1=T_2+V_2 \\
& 0+\frac{1}{2}(1.20)\left[\sqrt{(3)^2+(0.5)^2}-0.5\right]^2=\frac{1}{2}\left[\frac{50}{32.2}(0.7)^2\right] \omega^2+\frac{1}{2}\left(\frac{50}{32.2}\right)(1 \omega)^2 \\
& +\frac{1}{2}(1.20)(0.9292-0.5)^2 \\
& \omega=1.80 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
