Compound pendulum

  1. 1. The problem statement, all variables and given/known data
    I have calculated the value of the radius of gyration, k for a bar (and moment of inertia) and got three different values from three different methods. Now i need to determine which is the best value. I'm confused about how to do this, and how do i get the %uncertainty for k.

    Value of k/m [Moment of Inertia / kgm2]
    0.282 [8.93 x 10-3] (method 1)
    0.289 [9.37 x 10-3] (method 2)
    0.291 [9.49 x 10-3] (method 3)

    (sorry i tried to separate this but for some reason it didn't work, so i used brackets to try and separate them)

    Method 1 is from the intercept of the period squared x distance from centre of mass graph
    Method 2 is from the dimensions of the bar
    Method 3 from using the minimum time period


    2. Relevant equations
    T2D = 4/gπ2 D2 + 4/gπ2 k2 used in method 1

    D = distance from centre of mass
    T = radius of gyration
    k = radius of gyrat
    g= acceleration due to gravity

    k = (1/12)(l2 + w2)1/2 used in method 2

    k = (T2g)/ 8π2 used in method 3

    3. The attempt at a solution

    I don't think that the experimental value in method 1 is very accurate because of the problems in measuring the period, so would the best value of k be from method 2?
    Is there a set value that k is meant to be for a compound pendulum consisting of a wooden bar pivoted at different holes?
    I'm quite confused about this and would be really grateful for any help in understanding.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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