Physics Lab 7_ Rotation

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Dec 6, 2023

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Lab 7: Rotation Lab Date:4/8/2023 Lab Section #: _005____________

Purdue University Northwest – PHYS 15200 – Spring 2023 Abstract: In this lab, we aimed to determine how things such as inertia, torque, and angular acceleration are understood using a rotational inertia demonstrator. The rotating object comprises four pulleys of different radius, and four thin rods extending radially from the pulley. A "moveable mass" can be attached to each of the rods using a set-screw. As we noticed from the labs, as the masses are concentrated away from the rotational axis or center, the mass begins to carry more of the momentum, we saw that as angular acceleration decreases, inertia increases. Also when the mass is closer to the center, momentum is conserved and the object spins faster vs. as farther away the object spins slower. Although outside of this lab, moment of inertia does also determine the amount of kinetic energy that an object possesses from its rotational motion. The larger the momentum of inertia, the more energy is required to make the object spin faster or slower. Understanding the momentum of inertia is crucial in calculating the energy requirements and efficiency of various mechanical systems that involve rotational motion. In conclusion, by manipulating the demonstrator and observing its motion along with the various concepts it presents, we can develop a deeper understanding of these concepts and relate these to real-world scenarios. Introduction: The primary objectives of this lab experiment are: 1. To determine the moment of inertia of the spinning object 2. To modify the moment of inertia of the spinning object and moveable mass system and observe any changes in behavior 3. To compare the measured moment of inertia to a theoretical calculation 4. To adjust the torque on the spinning object and observe any changes in behavior. In this lab experiment, we will be using the Rotational Inertia Demonstrator to enhance our understanding of concepts such as moment of inertia, torque, and angular acceleration. The device consists of a rotating object that is affixed to a hub with low friction. The rotating object comprises four pulleys of different radius, and four thin rods extending radially from the pulley. A "moveable mass" can be attached to each of the rods using a set-screw. When we hang a "hanging mass" from a string wrapped around the pulley, the hanging mass produces tension in the string, which generates a torque on the system, resulting in the entire apparatus rotating. The torque can be adjusted by altering the suspended mass or the pulley that the string is wrapped around. Additionally, the moment of inertia of the system can be adjusted by moving the moveable masses.

To measure the system's behavior, we will observe the time it takes for a falling mass to descend a fixed distance. We can use these time measurements and the constant acceleration equations to compute the acceleration of the falling mass. We will then relate this acceleration to the angular acceleration and moment of inertia of the system. Experimental Procedure: To begin the experiment, the mass of the moveable mass and the hanging mass were taken using a scale, which measured the mass of the objects with a precision of 0.0g. Then, the diameter and radius of the two smallest pulleys were measured using a vernier caliper, which measured these values with a precision of 0.000cm. Next, all of the moveable masses were removed from the spinning apparatus so that the moment of inertia of the pulley and rods could be measured. A string was then tied around the smallest pulley and extended down just above the ground. The hanging mass, while not touching the ground, was tied to the end of the string. The distance between the bottom of the hanging mass and the bottom of the table was then taken using a tape measure with a precision of 0.0cm and recorded as the vertical displacement. The apparatus was then turned so the string would wind around the pulley until the bottom of the mass was even with the bottom of the table. Then, the apparatus was released so that the mass could fall and cause the apparatus to spin. The time that it took for the mass to reach the bottom was recorded by using a stopwatch with a precision of 0.00s. After conducting the test run, this same procedure was used and ten different trials were recorded. For these ten trials, the same setup as the test was used and the time it took for the weight to reach the bottom was recorded using a stopwatch. For the second experiment, one moveable mass is attached to each of the four rods as close to the center as possible. The distance between the center of the hub and the center of the moveable mass was then measured with a tape measure. Then, the same procedure in experiment one was repeated for five trials. The average of these times were then taken. After the five trials, the moveable masses were moved outward 5cm from the current position and the distance from the center of the hub and the moveable mass was measured again. Once again, the experimental procedure was repeated for five trails and the time that it took for the hanging mass to reach the bottom was recorded. The moveable masses were moved outward 5cm three more times and the same procedures were

followed each time. For the third experiment, the moveable masses were moved to the ends of each rod, and the distance between the rotation axis and the moveable mass was measured. Then, five trials were conducted using the smallest pulley and the times were recorded. Next, the string was wrapped around the second smallest pulley and five trials were conducted again. Data was recorded and compiled after each experiment. Various calculations were also done and are shown in the results and analysis section. Data: Setup: Measurement Symbol Value and measured unit Converted Value and SI unit Mass of one moveable mass Mm 185.6g 0.1856kg Mass of hanging mass Mh 200.2g 0.2002kg Diameter of smallest pulley D1 3.978cm 0.03978m Radius of smallest pulley R1 1.989cm 0.01989m Diameter of 2nd smallest pulley D2 5.556cm 0.05556m Radius of 2nd smallest pulley R2 2.778cm 0.02778m The weight values are recorded using a scale with a precision of 0.0g, and the length measurements are measured using a vernier caliper with a precision of 0.000cm. The conversion calculations are shown in the results and analysis section. Experiment One: Vertical Displacement of hanging mass = 83.8cm = 0.838m

This is the distance between the bottom of the hanging mass and the bottom of the table, measured using a tape measure with a precision of 0.0cm. The conversion is shown in the results and analysis section. Trial Time (s) 1 4.65 2 5.31 3 5.15 4 5.12 5 5.22 6 5.40 7 5.19 8 5.01 9 5.18 10 5.15 These are the time values recorded on the stopwatch for each trial in experiment one. Experiment Two: Distance between axis of rotation and center of moveable mass = 11.9cm = 0.119m This is the distance between the axis of rotation and the center of the moveable mass, measured using a tape measure with a precision of 0.0cm. The conversion is shown in the results and analysis section.

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