Experiment 8: Conservation of Angular Momentum

Experiment 8: Conservation of Angular Momentum

Authors: Lab conducted by Mohammed Karim (author), Richard, and Lynel.

Objective: Use conservation of momentum to find the angular acceleration of the disk.

Theory/Intro: During collision, we know that momentum is always conserved. Therefore, if we wanted to find the angular acceleration of a disk when being hit by a ball, we can find a solution if we have the velocity at which the ball hits the disk.

Apparatus/Procedure:

              

See pic of apparatus

               Our first step before calculating the angular acceleration, would be to calculate the velocity at which the ball hits the disk. We solved this by rolling the ball on the same ramp off the table and finding the distance it landed. (See Figure 19.1) After marking the distance from and height from the table and the carbon paper that the ball landed on, we could calculate the velocity through kinematics. The equation v=L/sqroot(2h/g) gave us a velocity of 1.3301 m/s. Next, after taking the measurements of the disk and finding the velocity, we could conduct the experiment. Using LoggerPro, we received a value of 5.5545 rad/s^2. (See Figure 19.2) We conducted multiple trial runs so we can see the affects of landing at different radii.

Data Tables:

Figure 19.1 - Drawing of setup with measurements

Figure 19.2 - Trial Run 1

Figure 19.3 -Trial Run 2

Figure 19.4 - Trial Run 3 ft. Prof Wolf

Analysis: We can see the relationship between angular momentum and the radius at where the ball lands. By doing many trials, we see that the further the ball goes, the faster the disk will spin. This is in line with what we know about torque. The further the force is applied on the radius, the more torque there is. We are able to determine values such as the gravitational potential energy of the ball. Starting from a height above due to the ramp, it definitely has potential energy. As it leaves, it has a velocity, therefore, it has a kinetic energy. Lastly, as it is rolling without slipping, it has rotational kinetic energy.

Conclusion: This experiment shows the conservation of angular momentum in a disk system. We understand that angular momentum is conserved, however, the analysis discusses energy, and the question to ask is, “Is energy conserved?” The answer to this question would be no. Especially in real life experimentation, energy is not conserved. For one, there is friction on the track that causes the ball to roll without slipping and occasionally slip. When the ball collides, energy is not necessarily conserved either as they ball collides into the platform and may have jolted or bounced and as a result, lost energy. Therefore, energy was not conserved.