Rotational Kinetic Energy & Moments of Inertia Lab Report

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University of Minnesota-Twin Cities *

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1301W

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Physics

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Dec 6, 2023

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pdf

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Rotational Kinetic Energy & Moments of Inertia Lab Report PHYS 1301W Professor Sulaiman TA: Mehmet Batu Bayindirli Evan Fang Lab XI November 13th, 2023 Abstract Vernier software was used to analyze the falling of the object. The objects measurements were vitaly in finding the experimental moment of inertia of the system. A video showed the hanging object as well showing the bottom of the ground. When the video started the hanging object went from rest to a velocity and that motion went into vernier software. That video was then determined to get our moment of inertia which was 0.127 kgm^2. The uncertainty for inertia was 0.113 kgm^2 and 0.145 kgm^2. To determine the uncertainty for moment of inertia, the only graph that is made needs to have a maximum slope fit and comparing the resulting moment of inertia and the "best" moment of inertia. Introduction In a university physics laboratory, a group of students embarks on an experiment to investigate the concept of moment of inertia. They explore how the distribution of mass in a rotating object affects its moment of inertia and subsequently, its rotational kinetic energy. The students use an apparatus that spins a horizontal disk, a ring and a pulley with mass on it to determine their experiment. Prediction The setup of this experiment can be drawn below. It models the disk(r2) and ring(r1) on the “A” base. It also shows the pulley and its string attached to both the “A” base and the hanging mass m.

The equation shows how to get the moment of inertia of the system experimentally. V^2max = ( 2mg / m + I /r1^2 ) h The bold part is the slope of the inertia with h as a x-axis and V^2max as y-axis. Procedure Three different videos were taken at different heights from each other. The vernier software then was used to determine the velocity and time from its different heights. The points can be taken right before it hits the ground since it only matters to get the velocity of the fastests it goes. The data is analyzed on google sheets and uses h as a x-axis and V^2max as y-axis to get the inertia. The default uncertainty for position was 0.005 meters. The uncertainty for velocity can be calculated with this equation: σV = σx / ∆t The uncertainty for V^2max can be used with this equation: σV^2max = 2VσV Analysis The result was that the moment of inertia was 0.127 kgm^2. The prediction proves to be right because the theoretical moment of inertia is 0.0118 kgm^2 which is close to the experimentally value of moment of inertia. The V^2max is 0.0106 m/s, 0.01 m/s & 0.007 m/s using vernier software. The uncertainty for V^2max is 0.0032 m/s, 0.003 m/s & 0.0022 m/s. Theses numbers came from this equation: σV^2 = 2VσV The uncertainty for velocity is 0.150 m/s. The uncertainty was determined with this equation: σV = σx / ∆t A potential error in the experiment could have been air resistance when the object goes down. The inconsistency of the object moving back and forth makes a potential error to note due to air resistance. All that togethers makes it difficult to get the right amount of moment of inertia. All objects have rotation and translation to each other, it’s important to know the rotational kinetic energy and moment of inertia of those objects. The group of students learned

how to calculate the moment of inertia with uncertainty in velocity and moment of inertia. They also learned how to make graphs and how rotation and translation relates to objects. The graph that gives moments of inertia with uncertainty. Conclusion The purpose of this lab was to experimentally get the moment of inertia of the system. The result was that the moment of inertia was 0.127 kgm^2 experimentally. The results were reasonable with the prediction since there was air resistance that affected getting the right amount of moment of inertia. The students learned the concepts of inertia and how to get it theoretically and experimentally.

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