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Angular Acceleration of a Pulley Supporting Two Hanging Masses

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi all! I'm working on a dynamics homework and have hit a wall here:

    d27a9810-5a81-45a4-b062-9839faa86a69-original.png

    "If the frictional moment at the pivot O is 2 N m, determine the angular acceleration of the grooved drum, which has a mass of 8 kg and a radius of gyration k = 225 mm.

    Ans: α = 0.622 rad/s^2 "

    2. Relevant equations

    M = m g r

    ƩM = I α

    I = m k^2


    3. The attempt at a solution

    The two masses exert moments about O, so my first step is to sum the moments about the pivot O:

    ƩM = (12 kg)(9.81 m/s^2)(0.2 m) - (7 kg)(9.81 m/s^2)(0.3 m)
    ƩM = 2.943 N m

    These moments are resisted by the frictional moment such that:

    ƩM = (2.943 N m) - (2 N m)
    ƩM = 0.943 N m

    Next we need the moment of inertia of the pulley:

    I = m_pulley * k^2
    I = (8 kg)(0.225 m)^2
    I = 0.405 kg m^2

    Finally we can solve for angular acceleration:

    ƩM = I α
    so
    α = ƩM / I
    α = (0.943 N m) / (0.405 kg m^2)
    α = 2.33 1 / s^2

    My analysis seems reasonable and I come up with the right units, but it is not very close to the given answer.

    Am I doing something wrong?
     
    Last edited: Apr 28, 2012
  2. jcsd
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