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 18 rpm in 11.0 s . Assume the merry-go-round is a uniform disk of radius 3.0 m and has a mass of 780 kg , and two children (each with a mass of 25 kg ) sit opposite each other on the edge.

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

Express your answer using two significant fi

What force is required at the edge?

Express your answer using two significant figures.

A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 18 rpm in 11.0 s . Assume the merry-go-round is a uniform disk of radius 3.0 m and has a mass of 780 kg , and two children (each with a mass of 25 kg ) sit opposite each other on the edge.

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

Express your answer using two significant fi

What force is required at the edge?

Express your answer using two significant figures.

Explanation / Answer

final angular speed = 18 rpm = 18 x 2pi rad / 60s = 1.88 rad/s

using wf = wi + alpha*t

1.88 = 0 + 11(alpha)

alpha = 0.171 rad/s^2

moment of inertia of system = (780 x 3^2 / 2) + (2 x 25 x 3^2)

                = 3960 kg m^2

torque = I alpha

      = 3960 x 0.171 = 677.16 Nm

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