Lab 7_ Moments of Inertia

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Temple University *

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1021

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Physics

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Apr 3, 2024

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Lab 7: Moments of Inertia Group Members: Joe Vlassakis, Amir Crump Goals: The Goal of this lab is to become familiar with how inertia affects your ability to change the direction of rotation of an object while using Newton’s 2nd law of rotational motion. Procedure: To start the experiment both of us grab the barbells placed on the lab tables and proceed to hold them out facing each other and begin to move the barbell back and forth in a twisting motion, then measure out to find the r or the radius and do it for both barbells. For part 2 we set up the rotational motion sensor, hung a 5-gram disk off of the sensor and created a graph on Pasco labeled for angular velocity vs time. Once you have set up the second part of the experiment you start the sensor and record the increase in angular velocity, once you have recorded the data for the outer radius position to the inner radius position collect all your data and plug the data into a table and answer the remaining questions Error and Precaution: The cause for error during the experiment could have come from miscalculation because one rounding error could be cause incorrect values Results:

Questions: Question 1. Both barbells have the same total mass, so what is it about Barbell 2 that makes it difficult to move quickly? The reason barbell 2 is more difficult to move than barbell 1 is because the moment of inertia is less Question 2. Recall that it takes more force to accelerate a larger mass for translational motion, which is explained by Newton’s 2nd Law: 𝐹 Net = 𝑚𝑎 . This law also holds in rotation form: 𝜏 Net = 𝐼𝛼 . In the rotational version of the law, force is replaced by torque 𝜏 , and acceleration is replaced by angular acceleration 𝛼 ; what takes the place of mass? The rotational inertia would take the place of mass. Question 3. Another group has hypothesized that adding 100 g extra mass to the center of the barbell where the hand is placed would have no effect on the ability of the person to rotate the barbell back and forth. Do you agree or disagree? Why? We agree with the group because adding 100 g extra mass would make the moment of inertia equal to 0 and r = 0 as well.

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Question 4. If you were to double the mass, but halve the radius of one of the barbells, how would the moment of inertia compare to the original value? The moment of inertia would stay the same Question 5. If you were a tightrope walker, which barbell would you rather be carrying? We would pick barbell 2 because the difficulty it would take to move the barbell would lead to less likelihood of movement occurring during the tightrope walking Part 2 Question 6. How did the angular acceleration change with the new moment of inertia? Was your prediction correct? They are inversely related: the larger the moment of inertia the smaller angular acceleration, and the smaller the moment of inertia the larger the angular acceleration. With the new moment of inertia in this experiment the angular acceleration doubled. Discussion: During the experiment we tested inertia and using Newton’s second law to IBB= 7.0*10^-7 kg*m^2 Id outer= 3.5*10^-5 kg*m^2 I Run 1 = 3.6*10^-5 kg*m^2 Id Inner = 1.8*10^-5 kg*m^2 I Run 2 = 1.9*10^-5 kg* T= .05*9.5*.0135 = .007 N*m^2 Run 1 angular velocity = 190 rad/s^2 Run 2 Angular velocity = 350 rad/s^2

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