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Moment of inertia problem

  1. Nov 5, 2012 #1
    1. The problem statement, all variables and given/known data

    A uniform beam of mass m = 0.6 kg and length L = 0.3 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 1.5 N, F2 = 1.5 N, F3 = 1.5 N and F4 = 1.5 N. F2 acts a distance d = 0.12 m from the center of mass.

    oxnartum.fa1.PNG

    What is the angular acceleration?

    2. Relevant equations

    I = Ʃmr^2
    I = ∫(r^2)dm
    α = Ʃτ/I

    3. The attempt at a solution

    I = (0.6 kg)(0.15 m)^2 +(0.6 kg)(0.12 m)^2 + (.6 kg)(0.15)^2 = 0.03564 kgm^2

    Ʃτ = 0.225 + 0.127 = 0.352 Nm

    α = 0.352/0.03564 = 9.88 rad/s^2

    This is apparently the wrong answer and I don't know where I messed up. [STRIKE][/STRIKE]
     
  2. jcsd
  3. Nov 5, 2012 #2
  4. Nov 6, 2012 #3

    haruspex

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    That formula is for an aggregate of point masses. For a continuous distribution of mass through a body, such as a solid bar, you need the integral formula below (or off-the-shelf solutions to it).
     
  5. Nov 6, 2012 #4

    tiny-tim

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    Hi Bishop556! Welcome to PF! :smile:

    (try using the X2 button just above the Reply box :wink:)
    The moment of inertia is a property of the body only

    it is completely independent of the forces acting on it, or of their positions. :wink:
     
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