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a yo-yo of mass 440kg measuring 0.9m in radius was dropped from a platform 63m high. One end of the string was tied to the platform, so the yo-yo unwinds as it descends. Assuming the axle of the yo-yo has a radius of 0.2m, find the velocity of descent at the end of the fall. The acceleration of gravity is 9.81 m/s^2.

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    The velocity of the yo-yo at any height is r*w, where w is the angular velocity and r = 0.2 m.

    Assume the yo-yo is a uniform disc, or pair of discs. Its moment of inertia is (1/2) M R^2, except for a small contribution for the axle, which we will have to ignore since they don't tell you its mass or length.

    After dropping a distance H, the potential energy loss equals the kinetic energy gain.

    M g H = (1/2)M V^2 + (1/2) I w^2
    = (1/2)M V^2 + (1/4)M R^2*(V/r)^2

    The mass M cancels out.

    V^2 = g*H /[1/2 + (1/4)(R/r)^2]

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