Moment of Inertia Lab Report

Moment of Inertia Abdallah Alazhari PHYS 141 TA: Marco Antonio Jimenez Due: 11/10/2022 Lab Partner: Carlos Ruiz Abstract The purpose of this lab was to measure inertia of three items: a solid disk, a rink and a bar. We were to determine how the moment of inertia changes as we change the length. A rotating stage was used for this experiment, with a PASO photogate to be able to measure its rotation. Introduction There were two parts to the experiment. The first part was to measure the moment of inertia for the solid disk, the bar, and the ring, and the second portion was to measure the change in the moment of inertia as we changed the length for the rotational portion. We also used different hanging masses to see if the moment of inertia increases as weight increases. A graph on excel was plotted for one over acceleration vs one over the mass to result in a linear graph.

Procedure For the first part of the experiment, we set up a rotating stage, smartgate photosensor, and the PASCO Capstone software. From here, we used the PASCO Capstone software to plot the angular velocity of each object over time, and took the slope as the acceleration. For the bar portion of the first part, we centered the bar so as to have an equal distribution of the weight, and started off with a hanging mass of 200g. We did five trials for this part, and then changed the radius at 12 cm with a hanging mass of 100g, and once again, did it 5 times. The same procedure was done for the wheel and ring , except the mass increased from 100g to 200g and finally to 300g, all with three trials each. From each of the trials with the different masses, we took the average of the five slopes (acceleration) to be able to use it in our plot. ❑ ❑ Theory Being able to guide to find the moment of inertia with the following equation: τ = T ∗ r = I ∗ α . From here, and the free body diagram from the moment of inertia, we know that this equation will be equal to: mg − T = m ∗ a = m ( α ∗ r ) T = mg − m ( r ∗ α ) Now, we are able to combine the equations to find the moment of inertia by doing the following : I = r ( mg − mr ) α Results and Discussion Spinning Wheel Hanging Mass , m(g) Slope (a) Average Slope Radius (m) Inertia

Hanging Mass m, (g) Slope (a) Average Slope (a) Radius (m) Inertia 100 0.7710 0.7673 0.1220 0.0087 0.7680 0.7630 200 1.6700 1.6733 1.7000 1.6500 300 2.3800 2.4967 2.5500 2.5600 Table 2: Values for the solid disk and an inertia of 0.0087. A key note here is that inertia is greater in the disk than it is in the wheel, even though they have the same mass. Graph 2 : Graph for solid disk yielding a 0.0073 slope. Conclusion

The purpose of this experiment was to measure the moment of inertia on three different object: a bar, a solid wheel, and a solid disk. The first portion of the experiment was to measure the moment of inertia on each, while the second portion consisted of measuring with different distances to see the change in inertia. Seeing as the disk and wheel had the same mass, but different inertia, we can conclude that distance and not mass is a factor in this. The disk had more inertia than the wheel because all of the mass is concentrated outside of its center, while the disk’s mass is evenly distributed. To improve the accuracy of this experiment, a constant speed or rotation of the object should be obtained that is by pulling a string or measuring the acceleration when it is constant.