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Homework Help: Period of a Pendulum and moment of inertia

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data

    A holiday ornament in the shape of a hollow sphere with mass 1.0×10−2 kg and radius 5.0×10−2 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum. Calculate its period. (You can ignore friction at the pivot. The moment of inertia of the sphere about the pivot at the tree limb is (5/3)MR^2.)

    2. Relevant equations

    T = 2Pi*(sqrt(I/mgL))

    3. The attempt at a solution

    This is the only formula I know for the period, but the problem doesn't give the value of L. Is there another formula for the period?
  2. jcsd
  3. Apr 27, 2010 #2


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    You're given enough info to figure out what L is. Think about what exactly L is defined as. It's the distance between what two points?
  4. Apr 27, 2010 #3
    I think it is saying that it is not hanging. It is attached by a loop. Draw a loop around the limb and then draw the ornament attached to the loop.
  5. Apr 27, 2010 #4


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    Hi Quincy! :smile:

    (have a square-root: √ and a pi: π and try using the X2 tag just above the Reply box :wink:)
    Then invent a formula! :wink:

    Find the torque (moment) of the weight at a typical angle, and then use the formula τ = Iα to get an (approximately) shm equation. :smile:
  6. Apr 27, 2010 #5
    Wouldn't you still need that distance for I?
  7. Apr 27, 2010 #6
    Oops, I misread the problem, I was thinking it was attached to a wire with some length instead of a loop.
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