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
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
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.