A 4.00 m radius merry-go-round has a mass 80 kg. A 50 kg person is standing on i

ID: 2035107 • Letter: A

Question

A 4.00 m radius merry-go-round has a mass 80 kg. A 50 kg person is standing on it at 3.5 m from the

axis. The merry-go-round has an initial speed of 0.50 rad/s. The person then walks towards the

center and stops when he is 0.5 m away from the axis. Calculate the new angular speed of the merry-

go-round, and the old and new linear speeds of the person.

Calculate Initial Moment of inertia of disk + person:

Calculate initial angular momentum:

Calculate Final Moment of inertia of disk + person:

Calculate final angular momentum:

Calculate new angular speed:

Calculate linear speeds of person:

Initial:

Final:

Moment of inertia of merry go round=80*4²/2=640 kg-m²

Moment of inertia of man about center=50*3.5²=612.5 kg-m²

Total initial moment of inertia =640+612.5=1252.5 kg-m²

Initial angular velocity=0.5 rad/s

Initial angular momentum=1252.5*0.5=626.25

Final moment of inertia of man=50*0.5²=12.5 kg-m²

Final momemt of inertia of system=640 kg-m²

Final total moment of inertia=12.5+640=652.5 kg-m²

Final Angular velocity =626.25/652.5=0.96 rad/s

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