A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then: A) mv/I B) v/R C) mRv/I D) 2mRv/I E) mRv/(mR²v + I)

Question

Quizplus · Accepted Answer

The angular momentum of the child before jumping on is mvr. After jumping on, the angular momentum of the system (child + merry-go-round) is (I + mR^2)ω. By conservation of angular momentum, mvr = (I + mR^2)ω, so ω = mRv/(I + mR^2).

A Playground Merry-Go-Round Has a Radius R and a Rotational