Aboy 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).

question: derive the expression for ωf in terms of the relevant quantities. express your answer in terms of i, m, r, v, and ωi.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants