A 27-kg boy stands 4 m from the center of a frictionless playground merry-go-round, which has a moment of inertia of 238 kg m2. The boy begins to run in a circular path with a speed of 0.6 m/s relative to the ground.

Question

(a) Calculate the angular velocity of the merry-go-round.

(b) Calculate the speed of the boy relative to the surface of the merry-go-round.

Answer 1

(a) Total angular momentum remains zero as the merry-go-round and the boy move in opposite directions.

M*V*R - I*w = 0
Solve for w

w = MVR/I = 27*0.6*4/238 = 0.27 rad/s

(b) Relative velocity to platform below the boy = V - (-R*w) = V + R*w