Lab report 8

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Florida Atlantic University *

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Physics

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Apr 3, 2024

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Experiment 8: Student name: Jordyn Kaliszewski Pre-lab section: 1) Introduction: In a paragraph between 100 and 150 words, explain the theory behind Experiment 8.1. (1 Point) In experiment 8.1, we need to understand the concept of a rigid body rotation about a moving axis. This concept states that any possible motion of the rigid body can be seen as a combination of translational motion of the center of mass and rotation about an axis. When a rigid object rotates, every part of it (every atom) moves in a circle, covering the same angle in the same amount of time, a. Every atom has a different velocity vector, b. Since all the velocities are different, we can't measure the speed of rotation of the top by giving a single velocity. We can, however, specify its speed of rotation consistently in terms of angle per unit time. Let the position of some reference point on the top be denoted by its angle 𝜃 , measured in a circle around the axis. We measure all our angles in radians. Then the change in the angular position of any point on the top can be written as 𝑑𝜃 , and all parts of the top have the same value of 𝑑𝜃 over a certain time interval 𝑑𝑡 . We define the angular velocity, 𝜔 [Crowell]. 2) Introduction: In a paragraph between 100 to 150 words, explain the theory behind Experiment 8.2. (1 Point) In experiment 8.2, we need to find the moment of inertia of a rigid body experimentally. When a body is free to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. The moment of inertia depends on how mass is distributed around an axis of rotation and will vary depending on the chosen axis [Moment of Inertia]. The formula we use to find the moment of inertia is 𝐼 = 𝑚𝑟 2 ( 𝑔 / 𝑟𝛼 − 1) Sources: https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Book%3A_Conceptual_Physics_(Crowel l)/05%3A_Conservation_of_Angular_Momentum/5.02%3A_Rigid- Body_Rotation#:~:text=When%20a%20rigid%20object%20rotates,by%20giving%20a%20single%20v elocity . https://en.wikipedia.org/wiki/Moment_of_inertia#:~:text=For%20an%20extended%20rigid%20body, from%20the%20axis%20in%20rotation .
3) Hypothesis: In an If /Then statement, highlight the purpose of the experiment. (1 point) 8.1 If we understand the concept, then we can study rigid-body rotation about a moving axis. 8.2 If we measure the moments of inertia of 3 different rigid bodies, then we can compare the measured/calculated results to determine the c values (of moment of inertia of the rigid bodies). Post-lab section: 5) 8.1 Discussion: In a paragraph between 100 and 150 words, explain what you learned. What conclusion can you draw from the results of this experiment? Answer the following questions with numerical values of experimental results and errors: (1 points) From this experiment, I can conclude that the speed does not depend on the mass or the radius of a rigid body. If the objects have the same c value, they will have the same speed at the bottom of the inclined plane. Since the solid spheres both have c=2/5, it didn’t matter if one was bigger, they both reached the bottom at the same time. However, when we race 2 objects with different c values, the object with the lesser c value reached the bottom first (I.e., solid sphere with c=2/5 beat the thin-walled hollow cylinder with c= 1). 6) 8.1 Conclusion: In one sentence, compare the results of the experiment with your Hypothesis. Why? Explain why the results you obtained either prove or disprove your hypothesis statement. (0.5 point) The results obtained prove my hypothesis, because once we understood the concept, we were able to study rigid-body rotation about a moving axis. 7) 8.2 Discussion: In a paragraph between 100 and 150 words, explain what you learned. What conclusion can you draw from the results of this experiment? Answer the following questions with numerical values of experimental results and errors: (1 points)
From experiment 8.2, I can conclude that the value of c affects the moment of inertia. Other factors that impact the moment of inertia include, the mass and size/shape of the object. The moment of inertia will increase when the mass distribution is dispersed farther from the axis of rotation. One thing that we noticed in this lab was when we did measurement 2 (system + sphere), the data was a little off as the sphere was hard to work with and gave our group lots of problems. When we compare our results to the example graph in the lab manual, we can see our results were off. 8) 8.2 Conclusion: In one sentence, compare the results of the experiment with your Hypothesis.Why? Explain why the results you obtained either prove or disprove your hypothesis statement. (0.5 point) The results obtained prove my hypothesis, as we were able to measure the moments of inertia of 3 different rigid bodies, then compare the measured/calculated results to determine the c values. 9) 8.1 Data Analysis with calculations: Attach an image of the lab manual pages containing tables with calculations in space provided on the table and with final calculations values. Measured values must contain units. Calculated values must contain proper number of significant figures and units. (1.5 points)
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10) 8.2 Data Analysis with calculations: Attach an image of the lab manual pages containing tables with calculations in space provided on the table and with final calculations values. Measured values must contain units. Calculated values must contain proper number of significant figures and units. (9.5 points)
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11) 8.2 End of Experiment Questions: Attach an image of the lab manual pages containing your responses to the end of experiment questions here. (2.5 points)

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