An object of mass m is sitting at the northernmost edge of a stationary merry-go-round of radius R. The merry-go-round begins rotating clockwise (as seen from above) with constant angular acceleration of \alpha. The coefficient of static friction between the object and the merry-go-round is \mu_{s}.
a. Derive an expression for the magnitude of the object’s velocity at the instant when it slides off the merry-go-round in terms of \mu_{s}, R, \alpha, and any necessary fundamental constants.
b. For this problem assume that \mu_{s}=0.5, \alpha=0.2 \mathrm{rad} / \mathrm{s}^{2}, and R=4 \mathrm{~m}. At what angle, as measured clockwise from north, is the direction of the object’s velocity at the instant when it slides off the merry-go-round? Report your answer to the nearest degree in the range 0 to 360^{\circ}.