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Homework Help: Rotational kinematics (mass wrapped around inner hub)

  1. Dec 10, 2014 #1
    1. The problem statement, all variables and given/known data
    A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of
    6.55 kg, a radius of R = 38.0 cm and is in the shape of a ring. A mass M = 1.85 kg is attached to
    the end of a string which is wrapped around an inner hub which has a radius r = 5.40 cm.

    Initially, the mass M is a distance h = 72.0 cm above the floor. [Assume friction is negligible!]
    a. What will be the resulting angular acceleration of this wheel?
    b. How long will it take for the mass M to reach the floor?
    c. What will be the total angular displacement of the wheel during the time in which the mass M
    is falling to the floor?
    d. How much work was done on the wheel by the external torque as the mass M falls to the floor?

    2. Relevant equations
    torque = FR = I * alpha
    F = Ma
    a = alpha * r

    I = mr^2 (told to ignore the spokes of wheel, same as hoop)
    3. The attempt at a solution
    I tried using T*R = I * alpha (T = tension, I = mR^2 where m is mass of wheel)
    and Mg - Ma = T and a = alpha *r

    I substituted for T, combined them together to solve for alpha,
    got alpha = MgR/(mR^2 + MR^2)
    which is 5.795

    however answer is 1.06rad/s^2. Can you help?
  2. jcsd
  3. Dec 10, 2014 #2


    User Avatar
    Science Advisor

    T*R = I*alpha? If I understand the problem description correctly, the tension T acts at a distance r from the hub, not R.

    That would explain why the answer you derived is independent of r while the real answer should depend strongly on r.
  4. Dec 10, 2014 #3
    that did it thanks! Mgr/(MR^2 + Mr^2) got me the answer
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