Name: Sherry Ye
Group Partners: Jae Yoo, Matt
Date: 31-Oct-2016
2. Purpose
In this experiment, we applied a known torque to an object that was rotating in order to determine the angular acceleration and found what kinds of factors affected the angular acceleration in part 1. Then, used the data we got from part one to determined the moment of inertia of each of the disks and disk combinations.
3. Introduction
In order to study what kinds of factors affected the angular acceleration, we did the same experiment in six times by changing the hanging mass, the radius of the torque pulley and the rotating mass. We changed the hanging mass with the same disk and same torque pulley; changed the torque pulley(the radius) with the same hanging mass and same disk; changed disk (rotating mass) with the same hanging mass and same torque pulley.
4. Apparatus/Experimental Procedure
1)Set up
Put the bottom disk and top disk together, but when we compressed the air, they need to rotate independently. The set up of the apparatus as shown. The pulley was tied on the top of the top disk with the string, which was hanging the mass that supplied with the apparatus. Hose clamp open for one disk operation, closed for two disk operation.
Opened logger pro in Rotary Motion and set the Equation in Sensor settings to 200 counts per rotation. Make sure the hose clamp in the bottom was open so that the bottom disk rotated independently of the top disk when the drop pin was in place. Turned on the compressed air that the disks rotated separately. With the string wrapped around the torque pulley and the hanging mass at its highest point, started the measurements and released the mass. Used the graphs of angular velocity to measure the angular acceleration as the mass moving down and up.
2)Procedure
We ran six experiments with variable changed:
EXPTS. 1, 2, and 3 were the effect of changing the hanging mass. Used the top steel disk and the small torque pulley, but the hanging mass was changed in double.
EXPTS. 1 and 4 were the effect of changing the radius and which the hanging mass exerted a torque. Use the top steel and the same hanging mass, but use small and large torque pulley.
EXPTS. 4, 5, and 6 were the effect of the rotating mass. Used same hanging mass and large pulley, but the disk were top steel, top aluminum, and top steel with bottom steel.
5. Measured Data
There was the data about the measurement of each disk.
6. Graphs/Calculated
We ran the experiments six times that we got six graphs of angular velocity and time in logger pro.
Here was graph we got from Expt. #1
For all graphs, we recorded the data from the graph of angular velocity and time in six different experiments. The slope of the graph was the acceleration of the hanging mass. The acceleration was going down, when it descended. The acceleration was going up, when it ascended. After we got the up and down absolute value of acceleration, we added both together to get the average of the acceleration.
7. Explanation
In the experiment 1, 2 and 3, we changed the hanging mass with the same torque pulley (radius) and disk (rotating mass). The result shows that angular acceleration was increasing, when the hanging mass became larger. In the experiment 1 and 4, we changed the torque pulley (radius) with the same hanging mass and disk (rotating mass). The result shows that angular acceleration increased, when the torque pulley became bigger. In the experiment, 4, 5, and 6, we changed the disk (rotating mass) with the same hanging mass and torque pulley (radius). The mass of the steel disk was bigger than the aluminum disk. The result shows that when the rotating mass became lager, the angular acceleration was getting smaller.
Also, we did some numerically specific calculation about the data as shown.
Part two:
In part two, we used the above data to calculate the moment of inertia of each of the disks. Before started, we assumed that there were no friction in the system, the equation of the moment of inertia of the disk is:
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m= hanging mass supplied with the apparatus
a= the average of the angular acceleration
r= the radius of the pulley
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Used that formula, we can get each of the disk the moment of inertia, and compared to the I=1/2MR^2, we did the calculation in expt. 5:
Continues to calculate the rest five experiments, we would get the table:
8. Conclusion
In this experiment, we found that the angular acceleration was affected by the hanging mass, the rotating mass and the radius of the torque pulley. The angular Acceleration was increasing when the hanging mass or the radius of the torque pulley became bigger. And, the angular acceleration was decreasing the rotating mass became lager. In part two, it was the good experiments, even though the different percent of the moment of inertia of the disk between experimental and theoretical was less than 10 percent. The friction force between the disks and pulley may caused the result different.
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