A small $8\mathrm{.}800-$lb collar C can slide freely on a thin ring of weight $12$ lb and radius $10$ in$.$ The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially the ring has an angular velocity of $35$ rad$/$srad$/$s and the collar is at the top of the ring $($ $=0$$=0)$ when it is given a slight nudge. The effect of friction is neglected.

Determine the angular velocity of the ring as the collar passes through the position $=90$$=90.$

The angular velocity of the ring as the collar passes through the position $=90$$=90$ is rad$/$srad$/$s