A merry-go-round in the park has a radius of 2.0 m and a rotation inertia of 800

Question

A merry-go-round in the park has a radius of 2.0 m and a rotation inertia of 800 kg*m^2. A child pushes the merry-go-round with a constant force of 50 N applied at a point tangent to the edge. A frictional torque of 8 N*m acts at the axle of the merry-go-round. What is the rotation acceleration of the merry-go-round while the child is pushing? At this rate, what will the rotational velocity of the merry-go-round be after 10 s if it starts from rest? What is the rotation acceleration of the merry-go-round if the child stops pushing after the 10 s? How long will it take for the merry-go-round to come to a stop?

Explanation / Answer

torque = I *

= 50*2 - 8 / 800 = 0.115 rad/s^2 while pusing

= t = 1.15rad/sec

if stops = - 8 / 800 = -0.01 rad/s^2 when left

t = 1.15/0.01 = 115 sec

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