Kevin Tran
Lab Partners: Kevin Nguyen, Jose Rodriguez
20 May, 2017

Angular Acceleration Part 1

Purpose: To find a measured value for the moment of inertia by applying torque to an object that can rotate and measure the angular acceleration, which gives us torque and acceleration data.

Introduction: We used a device that allows us to apply a know torque onto an object that can rotate. By allowing that to happen, we are able to measure the angular acceleration, which will eventually be used to measure values for the moment of inertia. The device we used is a system that requires air in order to activate. (picture below). In this experiment there are two disk stacked on top of each other that helped us get our results.

Before I can continue, I would like to note about the measurements and masses of the following equipment:
-the diameter and mass of the top steel disk: 1,357g, 126.5mm +/- 0.1mm, +/- 1g
-the diameter and mass of the bottom steel disk: 1,348g, 126.3mm  +/- 0.1mm, +/- 1g
-the diameter and mass of the top aluminum disk: 466g, 126.4mm  +/- 0.1mm, +/- 1g
-the diameter and mass of the smaller torque pulley: 9.99g, 25mm  +/- 0.1mm, +/- 1g
-the diameter and mass of the torque pulley: 36.3g, 48.9mm  +/- 0.1mm, +/- 1g
-the mass of the hanging mass supplied with the apparatus: 24.58g +/-1g

We plugged the power supply into the Pasco rotational sensor. We connected a cable to the Lab Pro at Dig/Sonic 1, so the computer is reading the top disk. We opened Logger Pros and went to our devices and chose "Rotary Motion" to give us a two graphs, which are the Angle(rad)/Time(sec) graph, and Velocity(rad/sec)/Time(sec) graph. In this case, we excluded the Angle(rad)/Time(sec) graph and used the Velocity(rad/sec)/Time(sec) graph. The reason for the exclusion is because of the poor timing resolution of the sensors. Then, we set up the equation in the sensor settings to 200 counters per rotation. 

Next, we turned on the compressed air so that the disks are rotating separately. With the string wrapped around the torque pulley and hanging mass at its highest point, we started collecting data with our loggers pro. 

Below are the data collection. First I would like to note that:

- Expt #1, 2, and 3: Effect of changing the hanging mass.

- Expt #1 and 4: Effect of changing the radius and which the hanging mass exerts a torque.

- Expt 4, 5 and 6: Effect of changing the rotating mass.

Below are the 6 graphs that helped my lab partners and I get our results. How we found angular acceleration for the downwards and upwards direction is by the slope in the graphs. The rising slope gives us the angular acceleration when it is going downwards and the descending slope gives us the angular acceleration when it is going upwards. How we found the average angular acceleration of each EXPT is by adding both the angular acceleration in the upwards and the downwards direction and divided by two.

EXPT 1:

EXPT 2:

EXPT 3:

EXPT 4:

EXPT 5:

EXPT 6:

Conclusion: In comparison to the first 3 EXPT, increasing the hanging mass only will increase the angular acceleration in the downwards and the upwards direction. In EXPT 1, the average angular is 1.148 rad/s^2. On the other hand, EXPT 2 is 2.24 rad/s^2, and EXPT 3 is 3.387 rad/s^2. To sum up, the change of mass in the hanging mass will increase angular acceleration. Now to compare EXPT 4 and EXPT 5. Next, changing the top disk will change the angular acceleration. When applying the steel disk on the top, the average acceleration is 2.192 rad/s^2. In comparison to the EXPT 5 with an aluminum disk on the top, the average angular acceleration is 6.186 rad/s^2. Note that the mass of steel disk is 1,357 g and the aluminum disk is 466 g. The change of rotating mass in the top disk tremendously affects the angular acceleration in the upwards and the downwards direction. In addition, changing the radius of the torque pulley does affect the angular acceleration. An error that might affect these results is the possible friction between the top and bottom disk when accelerating.