8-May-2017, 15-May-2017- Lab 16: Angular Acceleration

Lab 16: Angular Acceleration
May Soe Moe
Lab Partners: Ben Chen, Steven Castro, Stephanie Flores
Dates: 8-May 2015, 15-May 2015

Objective: To measure the angular acceleration of the rotating object by using torque and to determine the moment of inertia of the rotating disks used in this lab

Introduction:
In this lab, we will collect data in part 1 and figure out the angular acceleration of the rotating disk. In part 2, using the part 1 data, we will determine the moment of inertia.We are using two disks that will rotate and two different torque pulley on top that will hang a hanging mass with a string. For the first part to figure out the angular acceleration, we will apply various changes to the experiment. By applying these changes in six experiments, we can figure out how these changes affect the angular acceleration. In the first three experiments, we intend to observe the effect of changing the hanging mass. In the first and fourth experiment, we use two different hanging pulley with same mass. In the last three experiments, we will observe the effect of changing the rotating mass (steel disk to aluminum disk). We will use logger pro to record the angular acceleration during the disk rotation. For part two of the experiment, we will use the angular accelerations we got from the part 1 of the lab to plug into the moment of inertia equations for the disks that we derived in class.

Experimental Procedure:

Part 1:

(1) Our apparatus is as in the picture below:

Apparatus to measure angular acceleration

(2) We measured the masses and diameters of the rotating disks and torque pulleys.

(3) We used compressed air to let the disks rotate. As the disks rotate, the hanging mass that is wrapped around the torque pulley moves up and down.

(4) We connected the Pasco rotational sensor and Lab Pro to Logger Pro on a laptop to help us record the angular acceleration of the rotating disk as it is rotating and as the hanging mass goes up and down.

(5) After setting up, we did six experiments by changing the hanging mass, by changing the torque pulley with different radii, by changing the rotating disk between steel disk and aluminum disk.

(6) During this six experiments, we recorded the angular velocities of the rotating mass.

(7) We used linear fit to find the slope of the angular velocities and found the slope to be its angular acceleration. When the hanging mass goes up, the angular acceleration of the disk on the graph goes down. When the hanging mass goes down, the angular acceleration of the disk on the graph goes up.

Part 1 Data: 

Measurements of the rotating disks and torque pulleys

Hanging mass used and angular accelerations from our graphs during six experiments

Angular Acceleration of the Rotating Disk (slope m) from the Angular Velocity Vs. Time Graph [Experiment 1]

Experiment 2- Angular Acceleration of the Rotating Disk

Experiment 3

Experiment 4

Experiment 5

Experiment 6

Conclusion For Part 1: 
From our data, we found that the average angular acceleration of the experiment 2 and the experiment 4 are similar. We doubled the hanging mass for the experiment 2 and used the large torque pulley which has twice of larger radius than the small pulley. Increasing the hanging mass increases the angular acceleration of the rotating disk. In experiment 6, when both the top and bottom steel disks rotated, the angular acceleration slowed down by half than just the top steel disk rotating. When the rotating disk has smaller disk, in this case Aluminum disk, and the torque pulley with twice radius, the average angular acceleration of the disk got around three times faster.

Part 2:

Procedure:
The professor showed us how to derive the moment of inertia equation, involving the hanging mass and torque pulley in class. The expression we derived for the moment of inertia of the rotating disk is as below:

Derived Moment of Inertia of the rotating disk Equation

There is some frictional torque in the system since the rotating disk is not totally frictionless and we cannot neglect the mass of the pulley. We can confirm this by checking our angular acceleration values. We see that the ascending angular acceleration were not the same as the descending angular acceleration. Therefore, we used the first equation of the moment of inertia from the picture. The second equation is for when there is no friction involved in the system.

Part 2 Calculation: 

Calculation of Moment of Inertia of different disks in six experiments 

Conclusion:
When we looked at our experimental results of the moment of inertia of rotating disks, the first four experiments should have approximately the same results due to using the same torque pulley and the rotating steel disk. But the calculated moment of inertia of the disk for the first experiment was off by half of the moment of inertia of the disks of the second, third, and fourth experiments. The calculated moment of inertia of the second, third, and fourth experiment came out to be pretty close and consistent. The fifth and sixth experiment's moment of inertia of the disks also seemed reasonable.