28-Oct-2014: Angular Acceleration

Purpose:
The purpose of this lab is for students to explore torque and angular acceleration. By applying a known torque to a rotating object, we can measure the angular acceleration of the spinning object.

Apparatus:
With the Pasco rotational sensor connected to Logger Pro, we set up Logger Pro to only read the top disk. We also connected the air hose to the air supply, and turned the compressed air so that the disks can rotate separately. We attached the string to a hanging mass and a wrapped the other end around the torque pulley. The measurements start once we release the hanging mass at its highest  point, which should start pulling the pulley and spin the disks. The graphs reads angular velocity as the mass moves up and down.

Explanation:
With the apparatus all set up, we start the first 3 experiments with the small torque pulley with a diameter of 0.025 m and a mass of .001 kg. For trial one, we had the hanging mass at 25 g and only to top steel disk was spinning in this trial. The rotation was 1.069 rad/s going down and 1.213 rad/s going up, which averaged 1.141 rad/s. For trial 2, the hanging mass was doubled and only the top disk was spinning. The rotation was 2.096 rad/s going down and 2.495 rad/ s going up, which average 2.296 rad/s. The third trial had a hanging mass of 75 g and only the top disk was spinning at 3.274 rad/s going down and 3.507 rad/s going up. The average angular acceleration was 3.391. For the next trial, Trial 4, the hanging mass was 25 g, and the torque pulley was larger, with a diameter of 0.05 m and a mass of 0.036 kg. The top steel disk was spinning only, which spun at a rate of 2.072 rad/s going down and 2.258 rad/s going up. The average was 2.156 rad/s. The fifth trial has the same set up as trial four except for the fact that the top disk was aluminum instead of steel, making the spinning disk lighter. The angular acceleration 5.669 rad/s going down and 6.627 rad/s going up, which gave an average of 6.148 rad/s. The last trial, again, has the same setup as trial four, except for the fact that there are two spinning disks. The top steel and bottom steel are spinning together, which means more mass. The angular acceleration was 1.049 rad/s going down and 1.156 rad/s going up, and the average was 1.103 rad/s. The picture below shows most of the explanation from above.

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Trial 6

Conclusion:
According to trials 1 to 3, as the mass of the hanging mass increases, the angular acceleration increases. This is true because the heavier the hanging mass, the more force there is accelerating downwards, which gives more tension to the pulley, therefore giving more torque to the disk. Also, according to trials 1 and 4, the larger diameter of the torque pulley, the larger the angular acceleration. This is true because the larger the diameter of the pulley the more leverage there is for the hanging mass to torque the disk. Lastly, according to trials 5 and 6, the larger the mass that is spinning, or torquing, the smaller the angular acceleration. This is true because inertia depends on mass so the more mass an object has, the less angular speed the object has, and vise versa.