A 2.0m radius playground merry-go-round with a moment of inertia of 2000kg • m2

Question

A 2.0m radius playground merry-go-round with a moment of inertia of 2000kg • m2 is rotating freely with an angular speed of 1.0rad/s. Two people, each having a mass of 60kg, are standing right outside the edge of the merry-go-round and step onto it.

If one of the people now on the merry-go-round begins dragging a foot on the ground to bring the merry-go-round to rest, what is the force of friction present between their foot and the ground if the merry-go-round completes 3 revolutions while coming to rest?

Explanation / Answer

conservation of angular momentum used in first case

I*omega = (I + 2mr^2)*omega

2000 * 1 = (2000 + 2 * 60 * 4) * omega_new

omega_new = 2000 / (2480)

omega_new = 0.8 rad/s

total energy of merry go round system = 0.5 * I_tot * omega_new^2 = work by friction force

0.5 * 2480 * 0.8 * 0.8 = friction_force * (2 * pi * 2 ) 3

=> frction_force = 21.06N

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