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Torque and angular acceleration pulley problem

  1. Jul 12, 2014 #1
    1. The problem statement, all variables and given/known data
    A pulley in the shape of a cylinder of mass 5 kg and radius 0.6 m has a force of magnitude 30 N exerted tangentially on it. Find the angular acceleration of the pulley and its angular velocity after 3 s, assuming it starts from rest.

    2. Relevant equations
    T = Ftr
    T = mr^2a

    3. The attempt at a solution
    (a) I tried to find the acceleration using torque equations
    T = FtR
    T = 30(.6)

    T = mr^2a
    18 = 5(.36)a
    a = 10 rad/sec^2

    (b) Then I took the acceleration and tried to find the angular velocity
    ω = ωi + at
    ω = 10(3)
    ω = 30 rad/sec

    They correct answer is (a) 20 rad/sec^2 (b) 60 rad/sec
  2. jcsd
  3. Jul 12, 2014 #2
    You have used MI of a hollow cylinder whereas pulley is a solid cylinder .Use Moment of inertia of solid cylinder .
    Last edited: Jul 12, 2014
  4. Jul 30, 2014 #3
    I got it right. Thanks!
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