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

Question

A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 17 rpm in 10.5 s . Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 750 kg , and two children (each with a mass of 25 kg ) sit opposite each other on the edge.

Part A

Calculate the torque required to produce the acceleration, neglecting frictional torque.

Express your answer using two significant figures.

Part B

What force is required at the edge?

Express your answer using two significant figures.

Explanation / Answer

n = 17 rpm = 17/60 rps
= 2pi n
r = 2.5 m
M = 750+25+25 = 800 kg
I = Mr^2/2
t = 10.5 s
Angular acceleration = 2pi n/10.5
Torque = Fxr = Ix(angular acceleration)
.= Mr^2x2pi n /2x10.5= 423.6 N-m
F = Torque/r = 423.6 /2.5=169.4N

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