I am currently working on a physics project to experimentally confirm the relationship between mass and moment of inertia. The experiment is setup as depicted:
In this experiment, $r1$ and $r2$ are equal and constant. Attached to the pulley is a 0.1kg mass. As the mass falls the rod with the attached masses will rotate.
In this experiment, I record the time for 5 complete oscillations (ie. $θ = 10pi$) whilst changing the value of M1 and M2. (Note $M1=M2$)
I use this to calculate the angular acceleration ($α=2θ/t^2$) where $θ=10pi$ and $t$ is the average time for 5 complete rotations. I then use the equation $τ=Fr$ to calculate the torque where $F=mg=pullley Mass*9.8$ and $r=radius Of The Central Axis.$
Finally, I then use $I=τ/α$ to calculate the moment of inertia. Note this moment of inertia is for the masses as well as the rotating apparatus.
I then plot the calculated moment of inertia (units: $kgm^2$) against the total added mass (units: kg) (ie. M1+M2) and calculate the gradient/slope in $m^2$. This graph is linear with a non-zero intercept.
Is it possible with this data to confirm the directly proportional relationship between mass and moment of inertia? What should the square root of the gradient (units: $m$) correspond to?