The ball of mass m is guided along the vertical circular pathr = 2r, cos using the arm OA. If the arm has a constant angular velocity Ou derive a

formula for the angle o $ 45" at which the ball starts to leave the surface of the semi cylinder. Neglect friction and the size of the ball. The formula for the angle should be of the form: \theta=\tan ^{-1}\left(\frac{k r_{1} \theta_{0}^{2}}{g}\right) where k is a non-dimensional constant. Find k. 01 O2