11/9: Angular Acceleration

Title: Angular Acceleration
Purpose: The purpose of this experiment is to see what factors affect angular acceleration (Part 1), and determine the moments of inertia theoretically compared to experimentally (Part 2).
Apparatus:

The rotational sensor has two disks stacked on top of each other with another pulley to which a string is wrapped around and hung over with a hanging mass. Air is directed so that the disks can be (mostly) frictionless.
Theory:
The idea of this lab is to measure the angular acceleration of the hanging mass with varying hanging masses, size of the torque pulley, and the different disks. The ratio of the change in angular acceleration should be proportional to how much the variables differs from each other. For part 2, it we use the equation derived from the lab instructions and compare it to the theoretical inertia which is (1/2)MR^2.
Data:

    

Graphs/Calculations: 

Sample graph of how to obtain angular acceleration

Ratio of experiments 1, 2, and 3

Ratio of experiments 1 and 4

Ratio of experiments 4, 5, and 6

Ratio of experiments 2 and 4

Part 2 Calculations

Analysis: 

From the different ratios between all the experiments, we can see that a correlation appears. From experiments 1, 2, and 3, it appears that with twice the amount of hanging mass, the angular acceleration also increases by two. With three times the amount of hanging mass, the angular acceleration increases by three. From experiments 1 and 4, it can be seen that when the radius of the torque pulley increases, the speed also increases by almost the same amount. With experiments 4, 5, and 6, it can be seen that with the different masses of the steel and aluminum disks, the angular acceleration also varies by about the same amount. And from experiments 2 and 4, it can be seen that by changing the radius of the pulley as well as changing the amount of mass hanging produces about the same ratio. From the calculations of part 2, it can be seen that the theoretical inertias and experimental inertias are not that far away from each other.

Conclusion:
Sources of uncertainty and error may be from measuring the angular acceleration as we rotated the disks, as it is not completely frictionless. Our track in particular seemed to be especially rough, as the graphs proved to be a bit too jagged. Other sources of uncertainty may be from calculations and rounding off significant figures.