Rotational Motion

A thin but rigid semicircular wire frame of radius \(r\) is hinged at \(O\) and can rotate in its own vertical plane. A smooth peg \(P\) starts from \(O\) and moves horizontally with constant speed \(2 v_0\) lifting the frame upward as shown in figure. Find the angular velocity \(\omega\) of the frame when its diameter makes an angle of \(60^{\circ}\) with vertical.