A 35-kg child rides a playground merry-go-round, standing 1.6 m from its center.

Question

A 35-kg child rides a playground merry-go-round, standing 1.6 m from its center. The platform is initially at rest. A friend standing on the ground provides an angular acceleration of 0.12 radian/s^2 until an angular velocity of 1.1 rad/s has been achieved. What was the distance travelled by the child during this time? At the final angular velocity, what is the force of friction between the standing child's shoes and the merry-go-round platform?

Explanation / Answer

wf = wi +alpha*t => 1.1 = 0+ 0.12*t => t = 9.167 s theta =ut +0.5*alpha*t^2 => theta = 0+ 0.5*0.12*(9.167)^2 => theta = 5.042 rad distance travelled = 5.042* 1.6 = 8.067 m friction*r = I*alpha => friction*1.6 = (35*1.6^2)*0.12 => friction = 6.72 N

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