21-Nov-2016: Lab 20 Conservation of Linear and Angular Momentum

1. Title: Lab 20 Conservation of Linear and Angular Momentum
    Name: Qiwen Ye (Sherry)
    Partners: Matt
    Date: 21-Nov-2016

2. Purpose
In this experiment, we determined the angular velocity of  a rolling ball by using conservation of linear and angular momentum theorem and compared the theoretical and experimental values.

3. Introduction
In all the experiments so far, we had looked at the angular motion of an object rotating about some internal axis through its center of mass. This was an important type of rotation because any motion can be analyzed in terms of the translation of the center of mass and the rotation about the center of mass. However, in some instance it's more convenient to think in terms of rotation about a point external to the object. In this experiment, we would do that, investigating the conservation of angular momentum about a point that is external to the rolling ball.

4. Procedure
We did the lab together in the class, and Professor Wolf help us to set up the equipment (as shown in Figure 8.1) and record the data. Used the aluminum top disk, and mounted the ball center on top of the small torque pulley by using a gray-capped thumbscrew.

Determined the moment of inertia of the disk and ball catcher. Also, measured the mass of the ball.

Placed the ramp on the edge of a table, as shown. Determined the horizontal velocity of the ball as it rolls off the end of the ramp. First, marked a starting point on the ramp. Release the ball from this starting point and noted where the ball strikes the floor, and put the carbon paper on the floor. Measure the distance L and h. The horizontal velocity of the ball was then equal to L/t where t=2h/g.

5. Measured Data

Here was the measurement about the mass and the diameter of the ball; the diameter of the pulley.

6. Calculated Result

After we measured the data, we could find the moment of inertia of the system.

Then, used the conservation of angular momentum to calculate the angular velocity. 

7. Explanation
Compared the different percent between experimental and theoretical value for angular velocity, both different percent were less than 10%.

By the table, we found that once the radius of the ball getting bigger, the angular momentum would become larger.

8. Conclusion
In this lab, we studied the conservation of the linear and angular momentum theorem by calculating the angular velocity of the rolling ball. Also, we determined the relationship between the radius of the ball and the angular velocity that if the radius gets larger, the angular velocity becomes bigger.