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March 30, 2017

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1. A certain playground merry-go-round is essentially an 90-kg iron disk 2.0 m in radius. Two children, each with a mass of 46 kg, are originally standing on opposite sides of the disk near its outer edge. The merry-go-round is turning essentially without friction about a vertical axis once every 5 s. The children then clamber toward each other so that they are only 1.2 m from the center. What is its angular velocity now? (You do not need to specify its direction.)

  • Physics - ,

    Hint: Angular momentum is conserved.

    The initial angular velocity is
    w1 = (2*pi)/5 = 1.26 rad/s

    Moment of inertia of the platform is

    I = (1/2) M R^2 = 180 kg*m^2

    There is additional angular momentum due to the children. Conservation of angular momentum requires that:

    I*w1 + 2 m*5*2^2*w1 = I*w2 + 2*m*1^2*w2

    m is each child's mass. Solve for w2

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