Lab 7 Moment of Inertia

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Dec 6, 2023

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Lab 7: Moment of Inertia 03/27/21 Purpose : The objective of this lab is to see the effects of moment of inertia on one’s ability to change the direction of an object in rotation. This lab will also demonstrate how the geometric distribution of mass within an object will affect the moment of inertia. We will learn the relationship between moment of inertia and acceleration. Newton’s 2 nd law will be applied to understand ? = 𝐼? and how moment of inertia affects rotation. Apparatus : 2 barbells with different mass distributions, rotary motion sensor with attached ball- bearing disk and pulley, 4 ball bearings, a 5g mass hanger with masses, and computer with Capstone software and PASCO interface. Procedure : Part I :  One group member will rotate Barbell 1 (masses near center), while holding it at the center. Another group member will rotate Barbell 2 (masses at ends), while holding it at the center. Record difficulties and different sensations of holding and rotating both barbells.  Use meter stick to measure and record radius of both barbells. Part II :  Set up rotational motion sensor and rotary motion sensor. Hang 5g mass hanger from string for torque and rotation of system.  Use Capstone to activate rotary motion sensor. Then create a graph of angular velocity vs. time.  Position 4 balls on outer radius, record in Capstone, and release hanger. Than position the 4 balls on inner radius and make a prediction on the change in angular acceleration. Hit record in Capstone and release hanger.  Collect data with new moment of inertia, highlight data to get acceleration. Display runs and compare them.  Make excel sheet of data. With all of the data collected, calculate moment of inertia for ball bearings and disks. Then calculate torque. Finally, calculate angular acceleration using moment of inertia and torque. Data :

Precautions :  Make sure to measure the radius of ball bearings in the inner and outer positions correctly.  Make sure data is clearly defined for inner and outer position on graphs.  Make sure data is converted to appropriate unit of measure.  Use rotary motion sensor pulley radius when calculating torque for the force of gravity that is acting on the 5g hanger.  Make sure the motion sensor is set up properly to get accurate data.  Make sure the string on the pulley is positioned over the wheel correctly and without nicks. ` Questions : 1. Both barbells have the same total mass, so what is it about Barbell 2 that makes it difficult to move quickly ? Barbell 2 weights are further from the center which is the source of the force. Barbell 2 has a higher inertia value, which in turn will create a higher torque value. A higher torque value means an object will be harder to rotate, so because of this barbell 2 would be difficult to move quickly. 2. Recall that for translational motion it takes more force to accelerate a larger mass, which is explained by Newton’s 2nd Law: ? Net = 𝑚? . This law also holds in rotation form: ? Net = 𝐼? . In the rotational version of the law, force is replaced by torque ? , and acceleration is replaced by angular acceleration ? ; what takes the place of mass? Moment of inertia takes the place of the mass for the rotational version of the law. 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?

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I agree because we are not affecting the moment of inertia, just the mass. The inertia is still going to be zero. The addition of the 100 g would be evenly distributed and wouldn’t affect the person’s ability to rotate the barbell. 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? It will have no effect. The moment of inertia would be the same to the original value. 5. If you were a tightrope walker, which barbell would you rather be carrying? I would use barbell 2 because barbell 1 would be easy to rotate because it has a smaller inertia. With barbell 2, the mass is distributed away from the center giving the tightrope walker more time to correct their balance. 6. How did the angular acceleration change with the new moment of inertia? Was your prediction correct? My prediction was correct, that the acceleration would be faster when the moment of inertia was smaller. The acceleration was almost tripled for the inner radius position. Errors : When measuring the ball bearings for the inner and outer positions, we had problems getting precise recordings. However, I do not think it will mess with our data too much. Also, when dealing with Capstone, our computer had glitched. It had messed with our graphs giving us weird data, so we had to share data with the group that sat across from us. In addition, the excel data I received from the other group had to be changed. As you can see above in the excel calculation table, I had to write in some of the data. In general, other errors that could occur is the rotary motion sensor not capturing the data accurately. Or the string that’s a part of the pulley could be off track and affect the data. Conclusion : In part I, we learned that moment of inertia is depended on the size and shape of the object and the mass’s radius from the center. Barbell 2 had the weights positioned on the ends, so it had a larger moment of inertia and a slower acceleration. Barbell 1 had their weights positioned almost in the center, so it had a smaller moment of inertia and a faster acceleration. In addition, because of the greater moment of inertia means a greater torque and a smaller moment of inertia means a smaller torque. The higher the torque the harder to rotate and the smaller the moment of inertia means the easier to rotate.

Part II dealt with angular acceleration and inertia. With the use of the pulley, ball bearings, different radius lengths, and Capstone, we were able to define the relationship between angular acceleration and inertia. We found that a larger angular acceleration means a smaller inertia.

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