A boy of mass m is standing on the edge of a merry-go-round platform, which is initially rotating with a constant rotational velocity ωi (initial state). The rotational inertia of the merry-go-round is I, and the radius of the platform is r. After the boy steps down from the platform, tangentially to its edge, the merry-go-round continues rotating with a smaller rotational velocity ωf, and the boy continues moving away from the platform with constant speed v (final state).
Derive the expression for ωf in terms of the relevant quantities. Express your answer in terms of I, m, r, v, and ωi.