Conservation of ang momentum

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 21 November 2016 

conservation of ang mome

Mission Statement:To investigate the conservation of angular momentum about a point that is external to a rolling ball. Furthermore, to identify the angular velocity of the system after the ball is in the ball catcher by using the theorem of conservation of angular momentum.
Procedure and Analysis:
First, the apparatus, involving a track, metal ball , and spinning metal disk system, is shown below.

For this lab we conducted 2 trials, each with different radii, but not before collecting the required information, namely the diameter and mass of the steel ball.

Upon collecting this information, we needed to find the velocity of the ball when it left the track.
To do this, we employed kinematic equations using the measurements shown below. 

 Now equipped with the knowledge that the incoming velocity was 1.35 m/s,

next we set up the disk system and used logger pro to find the angular acceleration up and down.

 -we obtained two different places where the ball hit along with the omega that we would later need to compare, shown below.

 We also calculated the alpha, shown below.

armed with both the desired omega and alpha, we could now find the moment of inertia of the system, shown below.

Now equipped with the desired moment, we plugged into the conservation of angular momentum formula in order to find our theoretical omega, shown below.

 Conclusion:

As shown above, we found the percent error between our theoretical and experimental omegas to be 7.7% and 9.9%, respectively. Sources of this error likely involve the possibility that the collision between the ball and the arm was not, in fact, inelastic. Otherwise, we showed that angular momentum is conserved.