Experiment twelve_ Angular Momentum

Alexis Ortiz A20532815 Experiment 12 1. Answer the following questions using the data you acquired in this experiment: (a) Using the parallel axis theorem, write down the equations for the moment of inertia of a short disk attachment and the short cylindrical tube. Calculate the moments of inertia using the measured values of mass and radius. Moment of inertia of disk: 𝐼 ?𝑖?? = 1 2 ?? 2 = 1 2 (1. 3858?𝑔)(0. 228? 2 ) = 0. 0360 𝑁? 2 Moment of inertia of cylinder: = 𝐼 ?𝑦?𝑖???? = 1 2 ?? 2 1 2 (1. 4250?𝑔)(0. 106? 2 ) = 0. 00801 𝑁? 2 Moment of inertia total: 𝐼 ???𝑎? = 1 4 (? ?𝑖?? ? ?𝑖?? 2 + ? ?𝑦?𝑖???? ? ?𝑦?𝑖???? 2 ) = 1 4 ((1. 3858?𝑔)(0. 228? 2 ) + (1. 4250?𝑔)(0. 106? 2 )) = 0. 0217 𝑁? 2 (b) How well do the experimental values agree with the expected theoretical moments of inertia when calculated using the parallel axis theorem? (Part 1a): Using the equation and accounting for the radial fraction, the experimental 𝐼 = 𝑇 α moments of inertia were somewhat close to the theoretical value for moment of inertia. With a percent error ranging from 12.6-22.2%, some energy was likely lost due to drag, friction, the mass hanger behaving like a torsion pendulum due to uneveness in the z-axis, and the apparatus being unbalanced. (Part 1b): Using the same equation as in part 1a and accounting for the radial fraction, the experimental moments of inertia were much closer to the theoretical value for the moment of inertia of the combined disk and cylindrical tube. With the percent error ranging from 6.07-26.0%, the experimental data was more accurate with the calculated value but less precise. This lack of precision may be due to the cylindrical tube being unevenly distributed on the disk, the frictional force acting on the system, or errors in measuring the radii of the objects. (c) How well is the angular momentum conversed in the second experiment? Is this collision elastic or inelastic? Explain using energy relations. The angular momentum is fairly well conserved in the second experiment as the total mechanical energy is almost completely conserved. This can be seen with the addition of more weight proportionally decreasing the angular momentum as angular momentum is divided by the total weight of the system when the tube was dropped on the disk. (They are around the same weight, so the final angular velocity should be around half as much.) 2. In a clear and concise manner, describe your observations of the single ball experiment. Explain how the conservation of angular momentum can account for the behavior of the graph obtained. In the same manner, describe and explain your observations of the three-ball experiment. At first, the single ball spun with the apparatus, remaining at the top with the applied force being greater than the gravitational force acting on the ball, thus preventing the ball from falling down like it would without any angular motion. As the apparatus lost momentum (due to