Conservation of Linear and Angular Momentum

Purpose:
The purpose of the experiment is to test the understanding of all of the concepts that are involved in this collision. The concepts are moments of inertia, gravitational potential energy, torque, and the conservation of momentum.

Equipment Used:

The device is a series of two wheels one on top of the other that has air flow through it and creates a rotating system with a negligible amount of friction. The rotating system has a sensor that reads the rotation of the wheels, both the top and the bottom, since the two wheels can be made to either spin independently or together as a single system. The hanging mass is on a pulley that has a similar design, allowing air to flow through it to create a negligible amount of friction. A small attachment is placed on the device that is going to catch a ball that will be rolled down a ramp.

Data Collected:
A ball of mass .0238kg and radius .019m was rolled down a ramp. The end of the ramp was .975m above the ground and the horizontal distance that the ball rolled away from the end of the ramp was .51m. The height up the ramp that the ball was released from was .192m. Using this data, both the experimental and theoretical velocity that the ball should have can be calculated, but that will be done in the next section. The hanging mass on the system is .0247kg and it is tied around a disk that has a radius of .05m. The average angular acceleration with the disks and the attachment for catching the ball was 5.339rad/s^2. The experimental angular velocity of the system after the ball collided with the device was 1.572rad/s

Calculations:

These calculations are for calculating the experimental horizontal velocity of the ball as it leaves the ramp and the theoretical horizontal velocity of the ball. The experimental velocity was 1.14m/s and the theoretical velocity was 1.4m/s

These calculations are for calculating the moment of inertia of the device that will catch and rotate with the ball. The device is irregularly shaped so there is not formula for deriving the moment of inertia. It was calculated experimentally by comparing the torque and the angular acceleration of the moment of inertia. The moment of inertia was calculated to be .0011191kgm^2. Once the moment of inertia is calculated then a prediction for the angular velocity of the system after the collision can be made. The predicted angular velocity of the system after was 1.712rad/s and the experimental angular velocity was 1.572rad/s.








Conclusion:
The predicted angular acceleration had a percent error of 8.91%. The most likely source of the error is that the location of where the ball collided with the device wasn't exact and that the ball didn't collide exactly in a horizontal manner. That means that the ball was either on a slightly lowered or raised trajectory.

Sincerely,

Swaggy C