In the park, a mom pushes tangentially on a hand-drivenmerry-go-round and is abl

Question

In the park, a mom pushes tangentially on a hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 20 rpm in 10.0 s. Assume the merry-go-round is a uniform disk ofradius 2.0 m and has a mass of900 kg, and two children (each with a massof 20 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration,neglecting frictional torque.
1.                      m·N
What force is required at the edge?
2 N

In the park, a mom pushes tangentially on a hand-drivenmerry-go-round and is able to accelerate it from rest to afrequency of 20 rpm in 10.0 s. Assume the merry-go-round is a uniform disk ofradius 2.0 m and has a mass of900 kg, and two children (each with a massof 20 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration,neglecting frictional torque.
1.                      m·N
What force is required at the edge?
2 N

Explanation / Answer

time t= 10 s Initial angular speed w = 0 final angular speed w ' = 20 rpm = 20 * 2 rad / 60s                                   =1.047 rad / s Angular accleration = ( w ' - w ) / t                                 = 0.1047 rad / s ^ 2 radius of disk r = 2 m mass m = 900 kg mass of child M = 20 kg Total monentum of the disk -child system I = ( 1/ 2) m r ^ 2 +2Mr ^ 2                                                                 = 1800 + 160                                                                 = 1960 kg m ^ 2 we know torque T = I                              = 205.212 N m also we know T = Fr from this force F = T / r                           = 102.606 N

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