Lab 16 - Angular Acceleration

Purpose: To study how different factors affect the values for angular acceleration and moment of inertia. Then calculate values for the moment of inertia for different masses.

Apparatus: The setup that we used was a tabletop where metal disks can sit atop an axis of rotation that has compressed air flowing through it. The compressed air helps to reduce the amount of friction in the system and allows the metal disks to "float" freely about the axis. There are two disks, one steel one at the bottom and either a steel one on top, or an aluminum one on top. At the top of the stacked disks is a threaded hole where we were able to attach pulleys of varying sizes. The pulley then had a string with a hanging mass attached to it. The hanging mass was then hung off the edge of the table and let go in order to allow the system to accelerate. The string came off the disks horizontally, then changed direction to be vertical by way of another small, free-rotating pulley of negligible mass. The two larger metal disks each had 200 vertical stripes in order for a sensor on the setup to read how fast the disk was spinning. The data was then reported on a graph on logger pro.

Procedure: First thing I did was measure out all the diameters and masses of the disks, pulleys, and hanging mass.

Diameter and Mass
Top steel disk = 126.4mm, 1359g
Bottom steel disk = 126.4mm, 1347g
Top aluminum disk = 126.3mm, 466g
Small torque pulley = 24.9mm, 10.1g
Large torque pulley = 49.7mm, 36.1g
Hanging mass = 25.0 g

Comparisons: (Approximate ratios)
1) Ratio of small pulley to large pulley= 1:2
          Ratio of angular accelerations = 1:2
2) Hanging mass ratio 25g/50g = 1:2
          α = 1:2
3) Hanging mass ratio 25g/75g 1:3
          α = 1:3
4)Mass of top steel disk/mass of top aluminum = 3:1
          α = 1:3
5)Mass of top steel disk/top steel+bottom steel = 1:2
          α = 2:1
6) Diameter of small pulley/diameter of large pulley = 1:2
          α = 1:2

Experimental Angular accelerations:
1) 25g hanging mass, small pulley,top steel disk. Average α = 0.62295 rad/s/s

2) 50g mass, small pulley, top steel disk. Average α = 1.2495 rad/s/s

3) 75g mass, small pulley, top steel disk. Avg α = 2.259 rad/s/s

4) 25g mass, large pulley, top steel disk. Avg α = 1.2175 rad/s/s

5) 25g mass, large pulley, top aluminum.  Avg α = 3.4095 rad/s/s

6) 25g mass, large pulley, top+bottom steel disks. Avg α = 0.6109 rad/s/s

 This picture above shows all my calculations for the experimental moments of inertia for all of the disk combinations.

Conclusion: What I learned from my calculations of the moments of inertia are that although the angular acceleration can vary due to many factors such as radius, or torque, the moment of inertia still remains constant. This is important because it helped me see the connection between F=ma and T=Iα.
The moment of inertia remains constant in the experiments where the disk is the same, which is to be expected because the mass does not change just because it is being accelerated faster. The only thing that is different between a mass and a moment of inertia is that a moment of inertia takes into account the distribution of that mass along a radius. Some sources of error in this lab are the fact that none of these surfaces were frictionless, so we may have gotten smaller numbers for α, which meant that the moment of inertia was too large since we were dividing by α. Another source of error was that I was working alone with no lab partners for this experiment. Lastly, one more source is error is the fact that trying to get the right flow of compressed air through the system was kind of tricky, so it may or may not have skewed our results.