04-May-2015: Effects of mass and diameter variations on the angular acceleration of a spinning disk

     The purpose of this experiment was to determine what factors affect angular acceleration and to find a theoretical and experimental moment of inertia, and compare them, for the object in question.
     The object in question is a disk and pulley system. A disk lays flat with a torque pulley attached on top of it, and a string connected from the torque pulley over another pulley. The other side of the string has a hanging mass connected to it. A diagram is shown below.

The apparatus works by pushing air through it so the disks "float" on the air, making them nearly frictionless, similar to how air-hockey tables work. 

     Before the experiment began, measurements were made with calipers for the mass and diameter of each disk (there were 3, two steel disks and one aluminum), each torque pulley (a small and large one), and the mass of the hanging mass.

     Logger Pro was used to record the spin of the disks. On the side of the disks are 200 marks that a sensor reads and transmits to Logger Pro. This enables Logger Pro to produce graphs of angular position, angular velocity, and angular acceleration vs time as the hanging mass moves up and down. The angular acceleration vs time graph was useless due to the poor timing resolution of the sensors so it was not used. 

     Below is an example of one of the angular velocity vs time graphs used to find angular acceleration. Linear fits were used to find the slope, which was angular acceleration. Note that the positive slope was when the hanging mass was moving down and the negative slope was when it moved up. Each experiment gave similar graphs.

The average angular acceleration of the absolute values of the slopes from above was used. This was because of frictional complications in the system. As the mass moved down, torque from the string sped the disks up while frictional torque from the disks slowed them down. This means that angular acceleration as the mass descends is less than the ideal angular acceleration where there is no friction. Also, as the mass moves up, torque from the string slows the disks down and frictional torque also slows the disks down. This means that angular acceleration as the mass ascends is greater than the ideal angular acceleration where there is no friction. So, to compensate for this, the average angular acceleration was used.

     There were three factors that were changed over the course of the experiment. The hanging mass was varied, the radius of the torque pulley was varied, and the mass of the disks were varied. Below is the raw data table of the masses used and the angular acceleration numbers recorded by Logger Pro. The top of the picture has an explanation of what was varied with each experiment.

     The data in the "average angular acceleration" column tells us a lot. The data shows heavier hanging masses result in faster angular acceleration. In this experiment, angular acceleration went up by 0.6 rad/s^2 for every 25 grams of hanging mass added. The data shows the larger torque pulley gives a faster angular acceleration. And finally, the heavier the disks, the slower the angular acceleration.