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Rolling yo-yo and weight

  1. May 28, 2008 #1
    1. The problem statement, all variables and given/known data
    a 16lb yo-yo is resting on a horizontal table and is free to roll. The dimensions are r = 4in and R = 12in and the radius of gyration about the CM is 6in. A cord is wrapped around the inner radius, the passes over a perfect pulley, and is attached to a 8lb block.

    Find acceleration of 8lb block and the tension in the cord

    (answers are 4.830ft/s^2 and 6.792lb)

    2. Relevant equations

    F = ma
    torque = I*alpha = F*moment-arm
    Iaxis = Icm + mh^2
    I = (radius-gyration)R^2

    3. The attempt at a solution

    there are two accelerations a1 (weight) and a2 (yo-yo).

    (16/32slugs)*a2 = T

    I at table contact point = 90slug*in^2

    net torqe at table contact point = 90slug*in^2 * alpha = T(12in - 4in)

    T = 11.25*alpha and 0.5slugs * a2 = T

    for weight, (8/32slugs)a1 = 8lb - T

    so far, I have 4 unknowns and 3 equations so I can't solve for anything. What equation am I missing? i dont know how to find a relationship between alpha and a2 (i thought a2 = 12in*alpha but that doesn't work out right).

    thanks in advance
  2. jcsd
  3. May 29, 2008 #2


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    Homework Helper

    Consider pure rotation about axis passes through contact point. the center of mass is 12 in from contact point.
  4. May 29, 2008 #3
    i found out what i was missing: an equation describing the relationship between the acceleration of the weight and the accleration of the yo-yo.

    a-weight = a-yo-yo - R*alpha.
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