The three small spheres are welded to the light rigid frame which is rotating in a horizontal plane about a vertical axis through $O$ with an angular velocity $\dot{\theta}=20 \mathrm{rad} / \mathrm{s}$. If a couple $M_{o}=30 \mathrm{N} \cdot \mathrm{m}$ is applied to the frame for 5 seconds, compute the new angular velocity $\dot{\theta}^{\prime}$.