The Moment of Inertia of a Disk and a Ring

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Objective:
The objective of this laboratory was to theoretically calculate the moment of inertia of a disk and a ring and then to verify the moment of inertia for both objects through experiment. This laboratory shows that while the theoretical is not within the uncertainty of the experimental, both values are extremely similar to each other.
Data and Analysis:
Data:
Table 1: The Angular Acceleration of No Ring and Ring
Trial No Ring Ring
5g 4.57 ± 0.005 rad/s2 1.32 ± 0.005 rad/s2
10g 13.16 ± 0.005 rad/s2 3.09 ± 0.005 rad/s2
15g 20.45 ± 0.005 rad/s2 4.83 ± 0.005 rad/s2
20g 27.89 ± 0.005 rad/s2 6.60 ± 0.005 rad/s2
25g 35.65 ± 0.005 rad/s2 8.35 ± 0.005 rad/s2

Table 2: The Average Experimental and Theoretical Moment of Inertia for No Ring and Ring
Type Experimental Moment of Inertia Theoretical Moment of Inertia
No Ring 0.000198 ± 0.000047 kg•m2 0.000133 kg•m2
Ring 0.000631 ± 0.000101 kg•m2 0.000503 kg•m2

Analysis:
After completing the experiment, the data was transferred from DataStudio to Excel file, Lab9. Next, the points in the data when it started to increase were removed from the data points because that was when the 3-step pulley spun the opposite way of its original direction. This caused the mass hangar to be pulled back up and our experiment focuses on the just the drop. After deleting the excessive data, a scatter plot was created for all five trials for both the No Ring and the Ring. Then a trendline was added for the trials and the option to show the linear equation was selected. From the graph, the angular acceleration was determined by taking the slope from the equation shown on the graph of each trial.
After finding the angular acceleration, the experimental moment of inertia was calculated for all the tria...

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...ertia of the No Ring. The reason for this can be that the height of the 3-step pulley was changed during the experiment. Also, the angle of the clamp-on super pulley was changed in order to prevent the string from falling off the clamp-on super pulley during every trial. These are some of the things that were observed that have affected our results. There might multiple other changes that were done subconsciously by the experimenters without noticing.
In the future, the experiment can be improved by making sure that changes above, if required, are done before the first trial of the first run starts. Another problem was that the 3-step pulley moved slightly every time a trial was conducted. This could be prevented for the future labs by have a 3-step pulley that more resistible to movement. With these improvements, future laboratory might get more accurate results.

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