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Compound pendulum 
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#1
Apr2307, 01:11 PM

P: 41

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 / kgm^{2}] 0.282 [8.93 x 103] (method 1) 0.289 [9.37 x 103] (method 2) 0.291 [9.49 x 103] (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 T^{2}D = 4/gπ^{2} D^{2} + 4/gπ^{2} k^{2} 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)(l^{2} + w^{2})^{1/2} used in method 2 k = (T^{2}g)/ 8π^{2} 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 


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