Conservation of Linear and Angular Momentum

Purpose: The purpose of the lab was to see if the angular and linear momentum in a series of different circumstances including both types of motion.

Procedure: Below is the set up of how we had the first and second parts of the experiment set up. The second one in the picture below involved getting a ball and rolling it down from an initial height. Then it would roll down the ramp until it flew it off it and struck a certain point on the ground. The first part involved will allow us to acquire a final speed which in result leads on to the second part. In the second part, instead of the ball falling to the ground, the ball will fall into the ball catcher which is attached to a rotating apparatus and a hanging mass attached to the system as well. From this we will be able to calculate the rotational velocity of the disk and compare and see whether the linear momentum and rotational momentum are conserved.

Data; Since this lab was done in class everyone had gotten the same results. The picture above shows the different measurements that the professor gave to the class. This allowed us to get a final velocity for the system and recorded it as the final rotational velocity. The same data for when the ball was rolling down the ramp was also used.

The graph below shows the results of the disk spinning and the way the acceleration differs every time.

Calculations: The calculations below showed how we came the answer. For when the ball was rolling down the ramp we used Kinetic and Rotational Kinetic Energy and then once the ball left the ramp we used kinematics. The final velocity when the ball was off the ramp was 1.4 m/s and the final speed of the ball before it hit the ground was 1.11 m/s. 

Using the final velocity when the ball was initially off the ramp we were able to get the final rotational velocity of the disk when the ball struck the ball catcher. Using the moment of inertia of the disk and conservation of angular momentum of the impact we were able to calculate the final rotational velocity of the whole system.

Analysis: The differences between the actual and experimental values were really close. If I remember correctly we were below 5% as a class because the lab was done collectively.Overall it was a success because both the speed of the ball at launch and during the collision were very similar. This further proves the fact that linear and angular momentum are conserved if the speed of the ball initially is equal to the same amount in the final velocity.