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## Homework Statement

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 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

## Homework 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

## 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.