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Pulley, Moment of inertia, and acceleration

  1. Mar 29, 2005 #1
    A mass of .375kg hangs from a string that is wrapped around the circumference of a pulley with the moment of inertia = .0125 kg*m^2 and a radius of .26m. When the mass is released, the mass accelerates downward and the pulley rotates about its axis as the string unwinds. What is the acceleration of the mass??

    I have been using a=rF/mr^2, with my F=mg. The correct answer is 6.57m/s^2, but i can't seem to figure out why.

    No rush on answering, the question is from a practice exam I am studying.

    Thanks guys.
     
  2. jcsd
  3. Mar 29, 2005 #2

    xanthym

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    Science Advisor

    From the problem statement:
    {String Tension} = S
    {Mass of Suspended Entity} = m = (0.375 kg)
    {Weight of Mass} = W = (0.375 kg)*(9.81 m/sec^2) = (3.6788 N)
    {Cylinder Radius} = R = (0.26 m)
    {Cylinder Moment of Inertia} = I = (0.0125 kg*m^2)

    For the suspended entity:
    {Net Force} = ma =
    = W - S
    ::: ⇒ S = W - ma ::: Eq #1

    For the cylinder:
    {Net Torque} = Iα = I*a/R =
    = S*R
    ::: ⇒ S = I*a/R^2 ::: Eq #2

    Equating Eq #1 and Eq #2:
    W - ma = I*a/R^2
    ::: ⇒ a = W/{m + I/R^2}
    ::: ⇒ a = (3.6788 N)/{(0.375 kg) + (0.0125 kg*m^2)/(0.26 m)^2}
    ::: ⇒ a = (6.5702 m/sec^2)


    ~~
     
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