Angular Momentum Lab
Name: Kyle Collins
Lab Partner: Hunter McCabe
Date: 30 March 2015
Purpose: This lab's purpose is to demonstrate the conservation of angular momentum.
Theory: Angular momentum is defined as L=Iw, where I is the moment of inertia for the system and w is the angular velocity. Angulara velocity is also conserved, meaning that when solving for a variable, angular momentum can be set equal to angular momentum prime. For the system involved in this lab (with masses mounted at different and changing locations), the masses and radii for each are needed in the calculation for moment of inertia, as seen below.
Lab Partner: Hunter McCabe
Date: 30 March 2015
Purpose: This lab's purpose is to demonstrate the conservation of angular momentum.
Theory: Angular momentum is defined as L=Iw, where I is the moment of inertia for the system and w is the angular velocity. Angulara velocity is also conserved, meaning that when solving for a variable, angular momentum can be set equal to angular momentum prime. For the system involved in this lab (with masses mounted at different and changing locations), the masses and radii for each are needed in the calculation for moment of inertia, as seen below.
Experimental Technique: The entire system was affixed to a rotary motion sensor used to record angular acceleration. Using the slope of the angular acceleration vs. time in DataStudio, the angular velocity could be found. The system was spun by hand, and a pin system was used to allow the two central masses (designated m1 for calculations) to move radially outward and collide with the exterior masses, designated m2. Using all measured masses and radii, along with the angular velocity, the above equation is solved for angular momentum.
Data and Analysis: The radius of the rod was determined to be .19m and its mass was .027kg. Each central mass, or m1, was set .0365m away from the center of the rod, and each weighed .0741kg. The external masses, or m2, each had a mas of .0755kg and were set at .181m away from the rotation point. After the pin was pulled, the internal masses moved out to a distance .161m away from the rod's center. Since these will be important, the radius of the internal masses was initially 20.2% of the total radius, and after moving out measured in at 88.9% of the rod's radius. The external masses were a constant 95.3% of the total radius away from the center. This can all be written out in the following equation:
The low percent difference, which is easily accountable for in various error sources, confirms that angular momentum is indeed conserved.
Conclusion: The disk that the system sat on also had its own angular momentum which was ignored from calculations. The pin used to release the masses was not frictionless, and caused the masses to collide with the outer ones at slightly different times, possibly altering the angular momentum.
References:
http://lahsphysics.weebly.com
Giancoli, D., & Giancoli, D. (2000). Physics for scientists & engineers with modern physics (4th ed.). Upper Saddle River, N.J.: Prentice Hall.
References:
http://lahsphysics.weebly.com
Giancoli, D., & Giancoli, D. (2000). Physics for scientists & engineers with modern physics (4th ed.). Upper Saddle River, N.J.: Prentice Hall.