A teenager pushes tangentially on a small hand-driven merry-go-round and is able

Question

A teenager pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 12 in 9.9 . Assume the merry-go-round is a uniform disk of radius 2.3 and has a mass of 740 , and two children (each with a mass of 27 ) sit opposite each other on the edge. a)Calculate the torque required to produce the acceleration, neglecting frictional torque. b)What force is required at the edge?

Explanation / Answer

find the acceleration: 25 rpm = 25/60 rps --> f = 25/60 Hz (= frequency) ? = 2pi*f = 2pi*25/60 = 2,618 rad/s and acceleration a = ?/t = 2,618 rad/s/ 8 s = 0,32725 rad/s^2 ------- find moment of inertia I = 1/2 mR^2 for the disk, and 2*m*R^2 for the children. = 1/2*600*2^2 + 2*20*2^2 = 1360 kg*m^2 ---------- Torque t = F*R = I*a = 1360*0,32725 = 445,06 Nm Torque t = F*R = I*a = 445,06 Nm --> F = I*a/R F = 445.06 Nm/2 m = 225,529 N

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