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

Question

A teenager pushes tangentially on a small hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 17 rpm in 9.7 s. Assume the merry-go-roundis a uniform disk of radius 2.1 m and has a mass of680 kg, and two children (each with a mass of 30 kg) sitopposite each other on the edge. What is the torque required to produce theacceleration, neglecting frictional torque. What force is required at the edge? A teenager pushes tangentially on a small hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 17 rpm in 9.7 s. Assume the merry-go-roundis a uniform disk of radius 2.1 m and has a mass of680 kg, and two children (each with a mass of 30 kg) sitopposite each other on the edge. What is the torque required to produce theacceleration, neglecting frictional torque. What is the torque required to produce theacceleration, neglecting frictional torque. What force is required at the edge?

Explanation / Answer

Given that the initial angular velocity is 1 = 0       final angular velocity is 2 =17 rpm = 1.77 rad/s       Time taken is t = 9.7s       Radius of disk is r = 2.1 m mass of disk is M = 680 kg          mass of each child is m = 30 kg ------------------------------------------------------ The angular acceleration is = ( 2 -1 ) / t                                              =0.183 rad/s2 moment of inertia is I = (1/2) M*r2 +m*r2 + m*r2                                   = 1764 kg.m2 Torque is = I                   =322.81 N.m But the torque is = r*F                         F = / r                            = 153.72 N This the force required at edge.

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