Angular Momentum
Author: Jacob Hoffner
Partners: Zach Christoff and Alyssa Jordan
Date: March 2016
Partners: Zach Christoff and Alyssa Jordan
Date: March 2016
Purpose
To investigate the of Conservation of Angular Momentum.
Theory
According to the Law of Conservation of Momentum, Angular Momentum should be conserved when undergoing a collision. In this lab, a two point masses are connected on each end of a rod that has a point of rotation in the center. A separate mass on each side of the point of rotation is right against the center axle of the rod. During the initial angular momentum, the center two masses are released and become right next to the other masses on the outer ends of the rod, as indicated by the dottedlined squares above.
According to the Law of Conservation of Momentum, Angular Momentum should be conserved after the collision has occurred.
According to the Law of Conservation of Momentum, Angular Momentum should be conserved after the collision has occurred.
We must discover what I, or the Moment of Inertia, equals before and after the collision.
Lastly, we can derive an equation to prove the Law of Conservation of Momentum.
Kinetic EnergyWhen this collision takes place, the Kinetic Energy is greater in the final angular momentum than the initial angular momentum. By using the two equations to the right, we can discover this occurrence. By setting the Kinetic Energies equal to each other, we can show this comparison in Joule values.
We will discover if the final Kinetic Energy is greater than the initial Kinetic Energy. 

Experimental Technique
In order to conduct this lab, we first had to set up the device used to measure angular momentum. I clamped a sensor on a clamped rod in order to measure angular velocity in DataStudio. Then, a rod with six point masses was attached, three on each side. On each end, two of the masses were clamped onto the rod, while the other one on each side was loose. A string was attached to both of these loose point masses and fed through a makeshift pulley in the center.
Each point mass distance from the center of the rod was recorded, as well as their masses. The rod's length and mass was recorded as well. These measurement will be used in our derived equations.
During the experiment, the string was pulled in order for the two loose masses attached to be pulled from the sides of the rod with the clamped masses to the center of the rod. This creates a change in Moment of Inertia, which we can use to find a new angular velocity on DataStudio.
Using the change angular velocity found and the data collected on the rod and point masses, we can plug this information into an equation derived to find angular momentum. Finding the initial and final angular momentums allows us to prove out theory.
We can also use this information found to find the change in Kinetic Energy.
Overall, the pulling of the two loose point masses to the center of the rod changes the system's overall Moment of Inertia, ultimately changing the system's angular velocity. The collision allows the Moment of Inertia to decrease, which in turn allows angular velocity to increase. In order for angular momentum to be conserved, these value changes should make the overall system still equal the same angular momentum, therefore showing the conservation of angular momentum.
Each point mass distance from the center of the rod was recorded, as well as their masses. The rod's length and mass was recorded as well. These measurement will be used in our derived equations.
During the experiment, the string was pulled in order for the two loose masses attached to be pulled from the sides of the rod with the clamped masses to the center of the rod. This creates a change in Moment of Inertia, which we can use to find a new angular velocity on DataStudio.
Using the change angular velocity found and the data collected on the rod and point masses, we can plug this information into an equation derived to find angular momentum. Finding the initial and final angular momentums allows us to prove out theory.
We can also use this information found to find the change in Kinetic Energy.
Overall, the pulling of the two loose point masses to the center of the rod changes the system's overall Moment of Inertia, ultimately changing the system's angular velocity. The collision allows the Moment of Inertia to decrease, which in turn allows angular velocity to increase. In order for angular momentum to be conserved, these value changes should make the overall system still equal the same angular momentum, therefore showing the conservation of angular momentum.
Data
Below are the graphs that show the Angular Velocity found before and after the collision that took place.
Percent Difference in Angular Momentums: 0.9245%
Analysis
Below are the Sample Calculations for the following calculations:
(The equation for Angular Momentum was broken up into two separate equations so the math was not too involved so it was betterrepresented. Plus, this way each value of angular momentum can be expressed individually. The Kinetic Energies were done the same way.)
(The equation for Angular Momentum was broken up into two separate equations so the math was not too involved so it was betterrepresented. Plus, this way each value of angular momentum can be expressed individually. The Kinetic Energies were done the same way.)
Angular Momentum ~ Before Collision
Angular Momentum ~ After Collision
Percent Difference between the two Angular Momentums
Initial Kinetic Energy
Kinetic Energy ~ After Collision
Conclusion
In this lab, we were to investigate the conservation of angular momentum. We have discovered that angular momentum is indeed conserved, as the percent difference in the two angular momentum quantities was only a 0.9245% difference. Error in this lab that had created this percent difference could have been from several sources of error. Parallax error in measurements, such as the measuring of point mass distances from the center of the rod, could have resulted in possible error. Plus, the point masses were all considered the same mass, when some of them were different from each other by about 0.0001 kg. Other than these sources of error, the selection point of data on DataStudio could have been slightly off due to the data points given by the program. There is always friction on the system, however air resistance would have been so minuscule that it would not be a problem. Overall, error barely affected the outcome of this lab. The theory of angular momentum conservation was proven by this lab as well as the increase in Kinetic Energy, and is shown through the data collected. This lab was very successful.
References
Giancoli, Douglas C. "Angular Momentum; General Rotation." Physics for Scientists & Engineers with Modern Physics. 4th ed. Upper Saddle River, NJ: Prentice Hall, 2000. Print.
Bowman, D. (n.d.). Lahs Physics. Retrieved October 1, 2015, from http://lahsphysics.weebly.com/
Bowman, D. (2015, October 1). Chapter 11: Angular Momentum; General Rotation. Lecture presented at Physics, Lehighton.
Bowman, D. (n.d.). Lahs Physics. Retrieved October 1, 2015, from http://lahsphysics.weebly.com/
Bowman, D. (2015, October 1). Chapter 11: Angular Momentum; General Rotation. Lecture presented at Physics, Lehighton.