A disk with a mass of 29 kg and a radius of 31 cm is mounted on a frictionless horizontal axle. A string is wound many times around the disk and then attached to a 70-kg block, as shown in the figure. Find the acceleration of the block, assuming that the string does not slip.

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  1. R = .31 m
    Tension in string = T
    torque = T * R = I alpha
    so T = (I/R)alpha
    but a = alpha * R
    T = (I/R)(a/R) = (I/R^2) a

    force on block = m a = m g -T
    ma = mg - (I/R^2) a
    but I = (1/2) mdisk R^2
    m a = m g - (Mdisk/2) a
    70 a = 70*9.8 - 14.5 a
    solve for a

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