15-May-2017 Lab 16: Angular Acceleration Part 1

Lab 16: Angular acceleration Part 1

Kevin Nguyen

Lab Partners: Jose Rodriguez, Kevin Tran

Date Lab was performed: 15-May-2017

Purpose: This lab is designed to observe the effects of changing the hanging mass, torque pulley size, and weight of disk on the angular acceleration as the mass moves up and down. 

Theory/ Introduction: In this lab, we are trying to measure the effects of changing hanging mass, torque pulleys, and weight of the spinning disk on angular acceleration. On the apparatus, we know that there is a known torque acting on the rotating disk(s). This torque is represented by

where I represents inertia of the system and the alpha symbol represents the angular acceleration of the system.  Since torque is equal to 

we ran experiments to find the effects of doubling and tripling force, doubling the distance from the axis of rotation, doubling inertia, and dividing the value of inertia by 3 has on the angular acceleration.

Summary: First we used one of the apparatuses that were already set up.

We attached the cable coming out of the apparatus into the logger pro device, which is plugged into the computer.

When setting up the computer, we used rotary motion and set the equation of the sensor settings to 200 counters per rotation. 

We adjusted the hose clamp to test the bottom disk and top disk spinning before taking measurements. 

We measured the masses and diameters of the top steel disk, bottom steel disk, top aluminum disk smaller and larger torque pulley, and the mass of the hanging mass attached to the apparatus.

We then set up the apparatus and logger pro so that when the experiment starts, logger pro records the angular velocity of the spinning disk(s) when it is turning clockwise and counterclockwise. 

After doing so, we ran 6 separate experiments.

In the first experiment, we used only the hanging mass that came with the apparatus, the small torque pulley, and only the top steel disk was spinning. 

In the second experiment, we doubled the mass of the hanging mass, used the small torque pulley, and only the top steel disk was spinning.

In the third experiment, we tripled the mass of the hanging mass, used the small torque pulley, and only the top steel disk was spinning.

In the fourth experiment, we used the original hanging mass, used the large torque pulley, and only the top steel disk was spinning.

In the fifth experiment, we used the original hanging mass, used the large torque pulley, and only the top aluminum disk was spinning. 

In the sixth experiment, we used the original hanging mass, large torque pulley, and the top and bottom steel disk were spinning.

In each of these experiment, we recorded a angular velocity vs time graph.

Measured Data:

Average angular acceleration of 1st experiment

Average angular acceleration =  | angular acceleration down |  +  | angular acceleration up |  /2

                                                   =   | 1.061 rad/sec ^2 |  +  | -1.235 rad/ sec^2 | 

                                                   = 1.148 rad/second ^2

Calculated results:

Graph of 6th experiment

Graph of 4th experiment

Graph for 5th experiment

Graph of second Experiment

graph for 3rd experiment

Graph of 1st experiment

Explanation of Graphs:

The reason why we needed to graph an angular velocity vs time graph is because we are able to get the angular acceleration down and up by taking the slope of the line when the slope is positive (line is going upwards) and when the slope is negative (line is going downwards).

Conclusion:

For the conclusion, I'm using the first experiment data as the base to compare experiment's 2, 3 and 4 data to. The first experiment used a 24.6 gram hanging mass, top steel disk spinning, and small torque pulley. The 4th experiment is used as a base to compare experiment's 5 and 6 data to. Experiment 4 uses a 24.6 gram hanging mass, larger torque pulley, and top steel disk spinning.

In the second experiment, it seems that nearly doubling the hanging mass from the first experiment (from 24.6g to 49.6g) causes the average angular acceleration to approximately double from 1.148 rad/s^2 to 2.240 rad/sec^2.

In the third experiment, tripling the hanging mass from the first experiment from 24.6 g to 74.6 grams seems to triple the average angular acceleration from 1.148 rad/s^2 to 3.387 rad/s^2.

In the fourth experiment, it seems that using original hanging mass and the larger torque pulley (the larger torque pulley has 5.0 cm diameter, which is double the diameter of the smaller torque pulley) doubles the angular acceleration from 1.148 rad/s^2 to 2.192 rad/s^2.

In the fifth experiment, with the original hanging mass and larger torque pulley, using a lighter aluminum top disk that is 3 times lighter than the steel disk (466 grams vs 1362 grams) increased the angular acceleration 3 times the angular acceleration from the fourth experiment from 2.192 rad/s^2 to 6.1855 rad/s^2.

In the sixth experiment, with the large torque pulley (which doubled the torque value) and original hanging mass, we doubled the inertia of the system by having both steel disk (top and bottom) rotate. Having both disk rotate lead to making the angular acceleration nearly halved the angular acceleration from the fourth experiment (2.192 rad/s^2 vs 1.2745 rad/s^2)

Sources of uncertainty

One source of uncertainty is the frictional torque between the top and bottom disk. Since the disks aren't entirely frictionless, the frictional torque will lower the values of angular acceleration from what angular acceleration would be without friction.

Another source of uncertainty is that there is some air resistance acting on the hanging mass as it goes down and up, which can also decrease the angular acceleration of the system.

The pulley that the string lies on shown below

may also have friction acting on the string as the hanging mass goes up and down, causing the string to sometimes slip. The string slipping may cause the angular acceleration of the system to decrease.