Physics Lab 7

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Physics Lab 7: Rotation & Moment of Inertia Zyon Gomez, Allen Jones, Isaac McBride 03/02/2023

Introduction Lab 7: Rotation and Moment of Inertia will examine aspects of rotational kinematics. We will be measuring inertia, which is how much a mass can resist motion. We will be using a wheelie apparatus attached to a weight by string to see how the weight falls down. A timer is used to time how long it takes for the weight to touch the ground. This lab will be repeated a total of 5 times using 5 different weights. A theoretical and experimental value will be calculated and compared at the end of this lab. Purpose The purpose of Lab 7: Rotation and Moment of Inertia is to compare the moment of inertia between our theoretical calculations and the experimental values. Diagram

Data Drop time w/nothi ng added (s) Drop time w/ 270g block [24] (s) Drop time w/ 270g block [12] (s) Drop time w/disc (s) Drop time w/disc and circle (s) Trial 1 23.02 42.42 37.78 19.32 25.1 Trial 2 23.32 40.96 36.54 19.04 25.5 Trial 3 21.59 41.13 37.08 20.33 24.65 Ruler Mass (g) Ruler Length (cm) Circle Mass (g) Disc Mass (g) Outer Circle Radius (cm) Inner Circle Radius (cm) Disc Radius (cm) 561.1 50.5 1424.5 1440.5 6.1 5.6 11.15 Inertia of Ruler Inertia of Open Ring Inertia of Disk 2361.29 356.125 89543.28

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Sample Calculation Discussion and Error Analysis This lab had some room for errors to occur. For one, the string attached to the hooked object kept hitting the side of the apparatus. No matter how hard we tried to prevent this from happening, it still would occur. This error would be classified as a random error. Another error that occurred was the timer. It’s definitely impossible for us, humans, to perfectly time when the hooked object would start and end its journey to the floor. This could also be caused due to a delay on release or bad reflexes. Therefore, this would be classified as a human error. Both of these errors would affect our experiment’s measured values by slightly fluctuating the numbers, but nothing abnormally wrong.

Conclusion Within a rotating system, the moment of inertia depends on torque and angular acceleration. Torque increased just as angular acceleration did. In the second activity we also saw that the moment of inertia depends on how the mass is distributed about the axis. The moment of inertia will always be bigger if more mass is farther from the axis compared to if the same mass was distributed closer to the axis. Questions 1. What is torque? Give both the mathematical expression and an explanation in your own words. Give an example of an applied torque (from a situation unrelated to this lab), identifying the force and lever arm components. Torque is the measurement of the twisting force, or an amount of rotational force. T= r x F An example of applied torque is the force used when using a ratchet to unscrew a bolt. The lever arm components are the ratcheting piece of the tool, while the force is the arm pushing and pulling the ratchet. 2. How can you change the torque applied to a system? (There are 3 options). You can change the torque applied to a system by changing the force, changing the distance from the pivot to the force, and changing the angle of the applied force. 3. Derive an expression for the total magnitude of the acceleration of a point in a rotating body in terms of r, t and THETA a= r √(w^4+a^2)

4. Comment on any sources of error in the experiment. Express the relative error of each source as a percentage. Also express the total relative error as a percentage. The main sources of error involve human error or calculation errors. While releasing the mass hanger, there could be a delay before the person actually presses the timer if they do not have good reflexes. When performing calculations according to the formulas, there is always the off chance that one is performed incorrectly to the point where the result is wrong.

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