Angular Momentum Lab Report

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Stony Brook University *

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133

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Physics

Date

Jan 9, 2024

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pdf

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6

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Stony Brook University Department of Physics and Astronomy PHY 133 L08 Angular Momentum Lab Report Jake Stearns Lab partner: Robert Kulesza, Ahmed Abbasi TA: Mathieu Boisvert Experiment Date: 5 April 2023
Report Date: 12 April 2023 Introduction The purpose of the Angular Momentum Lab is to observe the principle of the conservation of angular momentum. To do this we used a rotating table that we would spin with a weight on a string connected to the table, and while it was spinning we would drop a weight on it. We could observe the conservation of angular momentum by watching the velocity of the table decrease as the mass increases. Theory The Derivation of Momentum of Inertia: Equation 2: I = mr(g - rα net )/αfr + α net Sum of Torques: T(torque) = T - Tfr Sum of Forces: F = mg - ma
Data Calculations To calculate the platform’s moment of inertia, we used the equation: using a net and a fr which were calculated by the computer when we spun the table, the hanging mass, the cylinder radius r, and acceleration due to gravity g, to get 1.757904588 kg*m/s. To
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calculate the uncertainty we did: (r uncertainty /r)*I to get 0.0037008518 kg*m/s. To calculate the disk’s moment of inertia, we used the equation: M is the mass of the disk, and R is the radius of the disk which were both manually measured we got the value to be 0.1337589609 kg*m/s. To get the uncertainty we used the formula: 1/2MR^2*SQRT((½σM/1/2M)^2+(2R2-1σR/R)^2) Finally, we calculated the total moment of inertia as 1.89 and the uncertainty as 0.027 by adding both of the already existing inertias and their uncertainties. Results Our initial angular momentum was 10.63 by multiplying the initial angular velocity and the platform inertia. To find our final angular momentum to be 7.41, we just added the total moment of inertia and final average velocity. Surprisingly our angular momentum was not conserved even though we expected it to be conserved. Error Analysis Systemic Error: Handle of the Disk: Since the disk is not a perfect disk and has a handle on the top, the center of mass is higher than it would be if the disk did not have a handle and this would change how the disk being dropped affects
the inertia. Systemic Error: Off-Center Drop: If the drop of the disk was off-center, the parallel axis theorem states the center of rotation would be in different places for both of them, and it should also be noted that the center of mass would be shifted for whole new system. This means that the value of inertia would be skewed and would be different than if the drop of the disk was perfectly aligned with the center of rotation of the already spinning table. Conclusion Our final angular momentum was not conserved within uncertainty which was not intended. We expected our angular momentum to be conserved and our data to show that. Some possible errors that could have occurred are interferences with dropping the weight, or friction.
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