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

Torque required is T = I*alpha

I is the moment of inertia of the system = (0.5*M*R^2)+(2*m*R^2) = (0.5*750*2.5^2)+(2*25*2.5^2) = 2656.25 Kg-m^2

alpha is the angular accelaration = (wf-wi)/t

Wf = 17 rpm = 17*2*3.142/60 = 1.78 rad/sec

Wi = 0 rad/sec

t = 10.5 sec

alpha = (wf-wi)/t = (1.78-0)/10.5 = 0.169 rad/s^2

then

Torque is T = I*alpha = 2656.25*0.169 = 448.9 N-m

B) But Torque T = R*F

Force F = T/R = 448.9/2.5 = 179.56 N

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