The figure shows a thin ring of mass \( M=1 \mathrm{~kg} \) and radius \( R=0.4 \mathrm{~m} \) s...

The figure shows a thin ring of mass \( M=1 \mathrm{~kg} \) and radius \( R=0.4 \mathrm{~m} \) spinning about a vertical diameter. (Take \( I=\frac{1}{2} M R^{2} \) ). A small bead of mass \( m=0.2 \mathrm{~kg} \) can slide without friction along the ring. When the bead is at the top of the ring, the angular velocity is \( 5 \mathrm{rad} / \mathrm{s} \). What is the angular velocity when the bead slips halfway to \( \theta=45^{\circ} \) ?