LAB 16 - Angular Acceleration
Tony Wu
October 31, 2016
Lab Goal: To understand the factors that affect the angular acceleration. To measure the angular acceleration of a pulley and hanging mass system. In part 2, we use our data to determine the moment of inertia of each other disks (or disk combinations).
Theory/Introduction: We applied a known torque to an object that can rotate. The known torque comes from the hanging mass that is attached to a pulley. When the mass descends, there is a torque applied to the pulley and the disks rotate. In this lab we recorded the changes in angular acceleration due to changing a few factors. In experiments 1, 2, and 3, we changed only the amount of mass hanging from the string. . In experiments 1 and 4, we hang the size of the torque pulley that the string is coiling around. In experiments 4, 5, and 6 we changed the mass of the rotating mass. For example, experiment 4 was a top steel disk, experiment 5 was a top aluminum disk, and experiment 6 was a top steel disk and a bottom steel disk.
Apparatus:
Theory/Introduction: We applied a known torque to an object that can rotate. The known torque comes from the hanging mass that is attached to a pulley. When the mass descends, there is a torque applied to the pulley and the disks rotate. In this lab we recorded the changes in angular acceleration due to changing a few factors. In experiments 1, 2, and 3, we changed only the amount of mass hanging from the string. . In experiments 1 and 4, we hang the size of the torque pulley that the string is coiling around. In experiments 4, 5, and 6 we changed the mass of the rotating mass. For example, experiment 4 was a top steel disk, experiment 5 was a top aluminum disk, and experiment 6 was a top steel disk and a bottom steel disk.
Apparatus:
We hang a varying masses from a string that is wrapped around a pulley. The pulley is attached to two disks that rotate freely. The disks are frictionless because air is flowing between the disks. The disks have 200 tick marks along the circumference of each disk. Logger Pro counts how fast the disks are turning due to the weight of the hanging mass traveling up and down. The angular acceleration of the hanging mass on the way up and down are recorded. The table of results below show the average angular acceleration. We repeat the process by changing different variables each trial. We change the weight of the hanging mass, the size of the pulley, and the type of disks that the pulley rests on.
Data and Calculations:
The "Mass" is the mass of the hanging weight. The "Radius" is the radius of the pulley, one small and
one large. The "Alpha" is the average of the angular acceleration on the way up and down.
The "Inertia" values are the values of inertia of each of the disks and combination of disks.
The experimental values of inertia come from the equation of
I_disk = mgr / [ ( |alpha_down| + |alpha_up| ) / 2 ] - MR^2
The theoretical values of inertia come from the equation I = MR^2
Note that the mass M and radius R in these equations are the mass and radius for the disks, not the pulley.
Conclusions:
Our results were fairly close. The discrepancy between the experimental and theoretical values come from multiple assumptions made during the lab. We assumed that the pulley, disks and string are all frictionless. We also assume that the disks are solid, uniform disks. In our lab, however, the disks have holes in the middle in order to lock the disks in place with a screw. We also assumed that the torque and friction are the same in all directions, independent of the angular speed omega. With these assumptions in mind, our results are still within a very good approximation.
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