#### Jumping on a Merry-Go-Round

Sarah, with mass m and velocity v, runs toward a playground merry-go-round and jumps on at its edge. Sarah and the merry-go-round (mass M, radius R, and moment of inertia I = cMR^{2}) then spin together with a constant angular velocity ω_{f}. If Sarah's initial velocity is tangent to the circular merry-go-round, what is ω_{f}?