Question

A child of mass m is playing on a merry-go-round which has mass 6m and radius r. Assume the merry-go-round is a uniform disk. The child is standing on the edge of the merry-go-round, which is spinning with an angular speed ω1.

a) What is the moment of inertia, I1, of the compound system (child + merry-go-round) about the center of the merry-go-round?

b) The child now walks halfway to the center of the merry-go-round. What is the new angular speed, ω2, of the compound system?

c) How much work did the child do in walking halfway to the center of the merry-go-round? Express your answer as a numerical fraction of the original kinetic energy, K1, in the compound
system.

d) A second child, also of mass m, initially standing at rest next to the merry-go-round, steps on to the edge of the merry-go-round (and nearly has her arms torn off in the process). What is the new angular speed, ω3, of the compound system? Express your answer as a numerical fraction of the original angular speed, ω1.

e) The second child now walks to the center of the merry-go-round. What is the new angular speed,ω4, of the compound system? Express your answer as a numerical fraction of the original angular speed, ω1.

Answer 1

a. add the two moments to gat combined.
b. momentum is conserved. compute the final moment.
final moment*wf=iniital moment(wi)
c. compute the final energy, and the initial energy, the kid did that as work.