Introduction
The goal of this experiment is to find the rotational inertia (I), also known as the moment of inertia, of various objects as they are being spun.
mg-T=ma → T=mg-ma
a=αR
τ=RxF=Iα
I=Rmgα-mR2
I=mR2
Procedure
Experiment 1: Changing distance of mass from the axis
1) Let the hanging mass drop and rotate the platform
2) Graph ω vs. t to find α
3) Move the mass away from the axis
Experiment 2: Changing the axis of rotation
1) Let the hanging mass drop and rotate the platform
2) Lay the disk on the axis
3) Graph ω vs. t to find α
4) Stand the disk up
Experiment 3: Changing distance of disk from the axis
1) Repeat the first experiment using the disk laying down
2) Graph ω vs. t to find α
Discussion
Factors that determine the moment of inertia are the radius and the mass. The inertia is found by the equation I=mR2. Friction in the rotational platform must be subtracted from the hanging mass to plug into the equation. The friction error used in experiment one was 20g and 50g for experiment two. During the experiment these values were not actually tested, but they are very important to consider.
Changing the position of the disk proved that mass isn’t the most important part of the experiment. The same disk with the same mass was used and yielded much different values for the angular acceleration (alpha). This is mostly due to air resistance because the standing up trial had a lot more air resistance.
The slopes of the graphs of I vs. R2 should have been the masses. They weren’t! They were linear though, which is correct. There are many reasons for this, like the parallel axis theorem. Also, the inertia of the pulley and the axel must be subtracted from the results to improve the accuracy of the data.