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Period of a Physical Pendulum

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A uniform metal disk (M = 9.81 kg, R = 8.99 m) is free to oscillate as a physical pendulum about an axis through the edge. Find T, the period for small oscillations.


    2. Relevant equations

    I (uniform disk, with axis through center of mass) = (1/2)MR^2
    T = 2π√(I/mgd), where d = distance from center of mass to point of rotation (axis)
    I (uniform disk, with axis through the edge = (3/2)MR^2, after using Parallel Axis Theorem:
    I (center of mass) + Md^2, where d = RADIUS of the disk:

    3. The attempt at a solution
    Plugging in for T, we have 2π√(I/(9.81)(9.81)(8.99).
    After plugging in I = (3/2)*(9.88)*(8.99)^2, we can plug and chug away:

    T = 3.2 seconds, however, this was incorrect.

    I was wondering where I went wrong here, thanks again !
     
  2. jcsd
  3. Dec 4, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    You might find that fewer "finger" errors can creep in if you carry out more of the process symbolically before plugging in numbers.

    Put your expression for the moment of inertia into the expression for the period and simplify before going numerical :wink:
     
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