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A teenager pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 12 in 9.0 . Assume the merry-go-round is a uniform disk of radius 2.2 and has a mass of 650 , and two children (each with a mass of 29 ) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque.

  • Physics -

    Step One: Convert rpm to radians per second

    (12 rpm)(2pi rad/1rev)(1min/60s) = 1.26 rad/s = w

    Step Two: Determine the Angular Acceleration

    w = alpha t + w

    1.26 rad/s = alpha (9.0 s) + 0

    Alpha = 0.140

    Step Three: Determine the moment of inertia of the disk and children

    Moment of inertia = Inertia of disk + inertia of child + inertia of child = 1/2mass of disk * r^2 + 2mass of child * r^2.

    So:
    I = 1/2(650 kg)(2.2)^2 +2(29kg)(2.2)^2

    Inertia total = 1573kg + 280.72kg = 1853.72 kg

    Step Four: Determine the magnitude of the torque.

    torque = Inertia * alpha

    torque = (0.140)(1853.72) = 259.5208

    So rounded, torque = 260 N.


    Some questions also required the following: What force is required at the edge?

    If so, force can be found using the following equation:

    torque = rFsin(theta)

    260N = (2.2)Fsin(90)

    Sin(90) = 1

    Therefore

    F = 260N/2.2

    F = 118N

    Hope that helps!

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