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Aidan Place Rotational Motion Lab Date 4/5/2023

The research question was what affects the inertia of the beam with mass on top of it? The evidence we found was according to our graphs while mass had a little effect the major effect was from radius and how far the mass was from the center of the beam.

While not having pictures of the other group boards the evidence comes to the same conclusion as we had another group check to make sure our graph was correct. Our scientific theory led us to create a math model that shows the best relation which was radius and mass. The whiteboard below shows what is math model we found looks like. I feel high confidence in the data we found in this lab. What makes me feel confident about this data is that we rechecked our math to make sure it made sense and redid any data that didn’t add up properly to the graph. We also made sure the graph was being done properly as we ran into problems with the graph. We ran into a systematic error where the machine that was recording the line making the data was not doing a straight line but a weird curve line but we were able to account for this error and get our data properly. Some assumption we had is that the weight on top will affect the inertia of the system more because more weight will cause it to speed up. For future work more tests should be done with the radius to see how it effect it with more accurate measurements. LAB 9 Name: Aidan Place Christian Radca

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Luke Hoover Lab 08: Rotation Part 2 3/29/2023 Physics Lab1 section 07 Point 2 Brainstorm Factor (complete list) The beam now has an added mass in which is at a distance R from the center of the beam, the moment of the inertia would change in turn of this and make the Inertia be overall be greater. 1. Mass 2. Distance (Radius) 3. Hang force Set-up(picture and labels) This experiment had one large beam on an axis of rotation in which a pulley was attached to the axis of rotation with a hanging mass connected to the axis of rotation. So, when the mass was pulled down by gravity the axis of rotation moved the entire system at the top.Now there is a mass on top compared to the first original experiment. More detailed pictures of the system are below:

Experimental Design (1 st Facot) Experimental Design Template Research Question: What factors impact the moment of inertia of a rotating system? Dependent variable (DV): Moment of Inertia independent variable (IV): Mass Control Variables (CV)(include actual values) Distance 0.1 meters, and hang force 0.05 kg

Testable Hypothesis:(IV vs DV) When changing the mass of the system on the beam the moment of Inertia will be affected Prediction: When increasing the mass of the system the moment of inertia will also increase Data (organizes into a neat table, and labels values into units mass of holder inertia angle of acceleration uncertainty 1 0.1037 0.0302 0.4255 0.0015 2 0.2037 0.065 0.3881 0.0011 3 0.3037 0.1131 0.33266 6.6*10^-4 4 0.4037 0.1559 0.32098 9.8*10^-4 5 0.5037 0.2118 0.29469 6.9*10^-4 Estimation of Uncertainties (estimates for each type of measurement, describes how uncertainties were determined) For the measuring if masses we had a .1 g for uncertainty and for measurements with the ruler we had a .1 meter difference. Graph (clearly labels with trendline and R^2) Figure 1

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Experimental Mathematical Model (in terms of IV and DV and description about relationship, describes possible physical meanings for the constants in experimental model) Looking at the y=0.4541x-0.0227, you pick out the 0.0227 which is close to the desired relationship of the model if you show it as the IV and DV, which it direct since IV and DV is inertia. Claim (in reference to research questions) Mass has a positive correlation with the moment of inertia. So, when held at a constant distance the increasing mass will then in turn increase the moment of inertia. Conditions of Claim (clearly Stated) The radius is being held constant; the hanging mass remains constant, and to the best of abilities there are no other factors affecting the system. Factor 2:(Radius) Experimental Design (2 nd Factor) Set-up (picture and labels) This set up is like last experiment when the mass was tested, but there is a slider in which the mass is slowly moved down the track so then different radius can be tested throughout the experiment.

Experimental Design Template Research Question: What factors impact the moment of inertia of a rotating system?

Dependent variable (DV): Moment of Inertia independent variable (IV): Radius Control Variables (CV)(include actual values) Mass, weight of beam Testable Hypothesis:(IV vs DV) When changing the radius of the weight set on the beam the moment of Inertia will be affected Prediction: When the radius is shorter the inertia will be greater Data (2 nd Factor)(organizes into a neat table, and labels values into units mass of holder(kg) inertia angular acceleration uncertain ty radius(c m) 1 0.5 0.003184 0.1592 0.0022 20 2 0.5 0.002148 0.1909 0.0019 15 3 0.5 0.001389 0.2778 0.0018 10 4 0.5 0.044325 0.3546 0.0016 5 5 0.5 0.4315 0.4315 0.0015 0 Estimation of Uncertainties (2 nd Factor) (estimates for each type of measurement, describes how uncertainties were determined) For the measuring of masses, we had a .1 g for uncertainty and for measurements with the ruler we had a .1-meter difference. This is due to the significant figures of the measuring devices we used the ruler that was attached to the slider. Also, we used the scale which, like the first experiment, was approached the same way. Graph (2 nd Factor) (clearly labels with trendline and R^2)

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Figure 2 Experimental Mathematical Model (2 nd Factor) (in terms of IV and DV and description about relationship, describes possible physical meanings for the constants in experimental model) Figure 3 Our experimental mathematical model is shown below the theoretical mathematical model on the white board in Figure 3 . When substituting the moment of inertia for y (dependent variable), and radius for x (independent variable), it can be seen that 0.5 represents mass and 0.0123 represents the moment of

inertia for the beam only. This is due to dimensional analysis as the units on one side of the equation must match the units on the other side. Claim (2 nd Factor) (in reference to research questions) Our claim is that the radius affects the total moment of inertia. Specifically, radius has a positive correlation with the total moment of inertia; as the radius increases, so does the moment of inertia. Conditions of Claim (2 nd Factor) (clearly Stated) The conditions for our claim are that the moment of inertia for the beam must remain constant as well as the hanging mass that is responsible for the torque. Assumptions Behind Claim (for both factors) Ignoring friction, the beam with weight increased momentum, and all other factors remained constant throughout the experiment, besides the specific factors that are being tested. So, when the radius and mass were tested, then all other factors that were tested were held.

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