Lab 15: Angular Acceleration

Physics Lab #15 started on 5/4/15
Angular Acceleration
Annemarie Branks
Professor Wolf

Objective: Find the angular acceleration for differing disks with an applied torque and determine their moment of inertia.

Part 1:

Procedure: 
     1.  The professor provided us with kits from which we will need a steel disk marked with an orange "this side down" sticker, an unmarked steel disk, an aluminum disk, a small pulley, a large pulley, and a hanging mass. The pulleys will be used as disks rather than pulleys. Measure all of these objects' diameters and masses.
Top steel disk - diameter: 12.644 cm; mass: 1360 g
Bottom steel disk - diameter: 12.640 cm; mass: 1348 g
Top aluminum disk - diameter: 12.640 cm; mass: 466 g
Small pulley - diameter: 252 cm; mass: 10.0 g
Hanging mass - mass: 24.9 g

In the picture, next to the kit there is the Pasco rotational sensor which pumps air in an effort to make the rotating disks frictionless. 

     2.  Connecting the Pasco to LoggerPro and its tube to an air valve, you can start collecting data at 200 counts per rotation. 

     Using the different pulleys, disks, and hanging masses we generate  angular velocity versus time graphs. Using those graphs we can find the angular acceleration from the graph's slope. But as you can see from the graphs below, there are two slopes. One slope is for when the hanging mass is going down and the other is for when it is going up. Here are a few of the graphs we generated but they look similar for all six experiments.

Experiment 4 with hanging mass only, large pulley, and the top disk steel.

 Experiment 5 with hanging mass only, large pulley, and the top disk aluminum.

Experiment 6 with hanging mass only, large pulley, and top steel moving with the bottom steel.

The data for experiments 1-6.

     From this data we can see that if the hanging mass doubles so will the system's angular acceleration. When the hanging mass triples the system's angular acceleration triples. So, from the first three experiments we see that for however many times the hanging mass is increased, then the system's angular acceleration increases by that much.

     When we increase the mass of the spinning disk, the angular acceleration changes. We can see from the data that when the top disk's mass is decreased by nearly three times, the system's angular acceleration increases nearly three times. When we nearly double the masses by having both disks spin at the same time the angular acceleration is two times slower. We can conclude from the last three experiments that for however many times the rotating disks' masses increase the angular acceleration decreases by that many times.

     3.  For further analysis and understanding, set up a motion sensor below the hanging mass and generate a velocity (m/s) versus time graph. When a linear fit is done, the slope should give a tangential acceleration of the system. Unfortunately, I did not get a picture of the graph with its linear fit but it seems that the acceleration of the hanging mass is about -0.050 m/s^2. This was done using the set up from experiment #4. 

We can confirm if this tangential acceleration is accurate by using the equation a(tangential)=α*r.  Alpha was 2.220 radians/s^2 and the radius of the large pulley was 0.0251 meters. This gave a tangential acceleration of 0.0556 m/s^2 which is pretty close to my "rise over run" method for determining the acceleration from the velocity graph.

Part 2:

Procedure:

     1.  We want to determine the moment of Inertia for each of the disks, but we need to consider frictional Torque. When we do consider frictional torque the moment of inertia is I = (mgr/α)-mr^2

The calculated Inertias show that changing the mass of the spinning disk changes Inertia most dramatically. Even the hanging mass differences do not seem to give much affect to the amount of force needed to get a disk moving. 

Sources of Error:

• There was uncertainty in the measurements of the disks' diameters due to human error and possibly error in the tool the disks were measured with
• The scales gave uncertainty in the masses. Our hanging mass was "supposed" to be 25 grams, but when weighed it gave a 24.9 gram measurement. 
• There is uncertainty when we assumed that the additional masses added to the hanging mass were each 25 grams.
• There is uncertainty in the accuracy of LoggerPro.
• The Pasco may have some degree of uncertainty when counting the marks on the disks
• There could be uncertainty in the number of marks on a disk. We simply trusted our professor who said there was 200 marks.
• The motion detector gives some uncertainty based on how accurate and quick it is.