Conservation Of Angular Momentum
Title: Angular Momentum Lab
Date: 3/17/15
Partner: Stephanie Kinsella
Date: 3/17/15
Partner: Stephanie Kinsella
Purpose
The purpose of this lab is to demonstrate the law of conservation of angular momentum within a collision.
Theory
The law of conservation of angular momentum states that for an isolated system, angular momentum is conserved in both magnitude and direction. In order to demonstrate this, the angular momentum needs to be calculated both before and after the collision.
We know the following are true:
We know the following are true:
Experimental Technique
The apparatus used to show the law of conservation of angular momentum is set up as shown below. Four masses are attached to the rod, which is screwed into a rotational motion sensor. Two of the masses are screwed to the rod flush with the end to keep them in place. The remaining two are let loose so as to allow the collision. They begin as far towards the middle as the motion sensor will allow. A wire is bent with a string tied in the middle so as to create a tool that keeps the masses in the center and releases them after an initial velocity is measured.
Using Data Studio and a rotary motion sensor, graph the velocity throughout the duration of the collision (example below). Begin spinning the device and, once it is steady, release the wire to let the center masses move to the outside. A change in velocity should be observed. Average the higher constant portion of the graph for the velocity before the collision and the lower constant portion for the velocity after.
Using Data Studio and a rotary motion sensor, graph the velocity throughout the duration of the collision (example below). Begin spinning the device and, once it is steady, release the wire to let the center masses move to the outside. A change in velocity should be observed. Average the higher constant portion of the graph for the velocity before the collision and the lower constant portion for the velocity after.
Data
The mass of object A was 75.3 g or 0.0753 kg.
The mass of object B was 74.0 g or 0.0740 kg.
The mass of object C was 73.8 g or 0.0738 kg.
The mass of object D was 75.3 g or 0.0753 kg.
The mass of the rod (object R) was 26.9 g, or 0.0269 kg.
The initial (and final, as they are stationary) radius of objects A and D was 18.0 cm, or 0.180 m.
The initial radius of objects B and C was 3.6 cm, or 0.036 m.
The final radius of object B and C was 15.9 cm, or 0.159 m.
The length of the rod was 38.0 cm, or 0.380 m.
The mass of object B was 74.0 g or 0.0740 kg.
The mass of object C was 73.8 g or 0.0738 kg.
The mass of object D was 75.3 g or 0.0753 kg.
The mass of the rod (object R) was 26.9 g, or 0.0269 kg.
The initial (and final, as they are stationary) radius of objects A and D was 18.0 cm, or 0.180 m.
The initial radius of objects B and C was 3.6 cm, or 0.036 m.
The final radius of object B and C was 15.9 cm, or 0.159 m.
The length of the rod was 38.0 cm, or 0.380 m.
The following initial and final angular velocities were recorded using a Data Studio graph:
Analysis
Using the derived equation, the momentum before the collision was calculated.
Then, the momentum after the collision was calculated.
Finally, percent difference was calculated between the two values.
The momentum before and after the collisions of each of the five trials as well as their percent differences are shown in the table below.
Conclusion
The purpose of this lab was to demonstrate the law of conservation of angular momentum in an experiment. In order to do so, we designed a collision and measured the velocity both before and after its occurrence, plugging the data into a derived equation to determine the momentum values.
Each trial was off by only 0.001 units. Due to the similarity in momentum values and the low percent differences, it can be concluded that the law of conservation of momentum was successfully shown.
The minimal amount of error could be attributed to our exclusion of the motion sensor in the system. When deriving the equation, we only accounted for the rod and four masses as our moving parts, when in reality the base of the motion sensor was also turning. A minute part of the momentum was likely transferred to the motion sensor where the kinetic energy was lost through friction.
Each trial was off by only 0.001 units. Due to the similarity in momentum values and the low percent differences, it can be concluded that the law of conservation of momentum was successfully shown.
The minimal amount of error could be attributed to our exclusion of the motion sensor in the system. When deriving the equation, we only accounted for the rod and four masses as our moving parts, when in reality the base of the motion sensor was also turning. A minute part of the momentum was likely transferred to the motion sensor where the kinetic energy was lost through friction.
References
Conservation Laws. (n.d.). Retrieved March 20, 2015, from http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html
Giancoli, D. (2009). Physics for Scientists and Engineers (4th ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.
Lahs Physics (n.d.). Retrieved October 6, 2014, from www.lahsphysics.weebly.com
Giancoli, D. (2009). Physics for Scientists and Engineers (4th ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.
Lahs Physics (n.d.). Retrieved October 6, 2014, from www.lahsphysics.weebly.com