Find Angular Velocity $\omega$

A bobbin rolls over a horizontal surface without slipping so that the velocity $v$ of the end of the thread (point A) is directed along the horizontal. A board hinged at point B leans against the bobbin. The inner and outer radii of the bobbin are $r$ and $R,$ respectively.

Determine the angular velocity $\omega$ (in rad/s) of the board as a function of the angle $\alpha$ , to two decimal places.

Details: $R = \SI{10}{\meter}, r = \SI{5}{\meter}, \alpha= 60^\circ, v = \SI[per-mode=symbol]{50}{\meter\per\second}.$