PHYS4A/ Fall 2014; Angular Acceleration

Purpose: This experiment was done to calculate the angular acceleration of disks of different masses and see how it affects the angular acceleration of an object.

For this experiment,  a hanging mass is attached to a pulley and a rotating disk. 

Experimental Set-Up

The bottom disk is a solid steel disk which has air flowing over its surface. The top disk is either an aluminum disk or a steel disk. The two disks can be made to either spin independently or together by allowing air to flow between them or directing the air through the holes. By using these techniques and understanding that torque in this case is equal to the radius multiplied by the force (tension).

Torque = r* T 

The set-up with the hanging mass

By changing different aspects of the experiment, we are able to see whether acceleration increases or decreases. Running the experiment with different parameters and recording all of the info, it is apparent that as the hanging mass increases, the angular acceleration increases. When the diameter of the torque pulley changes angular acceleration increases proportionally. The same is seen if the mass of the disks increase.

The angular acceleration  graphs were found using logger pro and taking linear fits of the angular velocity over time graphs like the one below. When looking at the acceleration, due to the orientation of the set-up, negative acceleration was the acceleration as the hanging mass moved up and the positive acceleration is when the hanging mass moves down.

Angular velocity vs Time for Trial 1

In the above graph, velocity is either increasing or decreasing at a steady rate meaning that angular acceleration is constant. This was done for each graph with the acceleration as the hanging mass went up, went down, and the two accelerations averaged to fill in the table above. The same thing was done for all six runs with similar graphs. The average acceleration is used because by taking the average, you are removing systematic error due to friction, making the results more accurate. The observations taken earlier support the equation given where

Torque = (radius)*(Tension) = (Moment of Inertia)*(angular acceleration)

or 

Tr = r*T = I(alpha)

This matches with the above observations where the radius of the of the pulley either got bigger or smaller and when the hanging mass changed which changed the tension in the string. The mass of the disks were changed to get different I's or moments of inertia. As masses increased, the moment also gets larger about the center of mass. Dividing torque by a larger I gives a smaller angular acceleration which was observed. This showed our experiment supports the theory and the experiment was a success.