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 the acceleration,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 the acceleration,neglecting frictional torque. What force is required at the edge?

Explanation / Answer

      Given that the initial angularvelocity 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                                              = ---------rad/s2 moment of inertia is I = (1/2) M*r2 +m*r2 + m*r2                                   = ------------- kg.m2 Torque is = I                   = --------- N.m But the torque is = r*F                         F = / r                            = ---------- N This the force required at edge.

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