Lab 8: Moment of Inertia State what you intend to accomplish with your experiment. What are you trying to measure? In this lab we are trying to find the relationship between linear motion and rotational motion. We are also trying to measure the moment of inertia of a rolling object by designing an experiment with several balls of different mass densities. Briefly describe how the apparatus will be used to make the measurement. A well-labeled photograph or diagram is an efficient way to explain the details of the experimental setup. We used three balls. One is a filled ball, a hollow ball and a mystery ball. We know the C values of the filled ball and of the hollow ball and we are trying to find the C of the mystery ball. Using a ramp and a photogate, we set the ramp at five different heights and took three trials at each height for each ball. The photogate recorded the velocity. Using the slope of the graph with the correlating height and velocity per ball, we can calculate C as the slope = 2g/c - 1. Analyze your data using well-formatted plot(s). Describe the models that were used to make sense of your data. The graph plots the velocity squared of each ball at different heights and the LINEST represents the slopes of each line and the intercepts. The blue line represents the equation for the filled ball, the grey line represents the mystery ball and the orange line represents the hollow ball. The filled ball has the fastest velocity and thus, the highest slope with the mystery as the second fastest and the hollow as the slowest. Clearly state the final result(s) of your experiment with an associated uncertainty estimate. Report your result with measurement units and the appropriate significant digits. Knowing that the slope = 2g/ c – 1 we were able to calculate C. For the filled ball, C is equal to 0.383 +- 0.032. For the hollow ball, C is equal to 0.641 +- 0.020. For the mystery ball, C is equal to 0.550 +- 0.040. Compare your result to another relevant quantity. For example, you might compare your measurement to an accepted value or another group’s value. Choose the best tools available to make the comparison meaningful. The accepted value for C for the filled ball is 0.4. Error: ( 0.383-0.4 ) / 0.4 = 0.0425. We were very close, with our results differing by 4 %. The accepted value for C for the hollow ball 0.67. Error: ( 0.641-0.67 ) / 0.67 = 0.043. We were very close, with our results differing by 4 %. The group in front of has a C value for their mystery ball of 0.532. Error: (0.559 – 0.532) / 0.532 = 0.05. Our results differ by 5 %. Identify and discuss the dominant source(s) of uncertainty in your result. A dominant source of error would be when getting the velocity of the balls because the balls can hit the side of the ramp which would slow it down. This would then affect the C value as the C values are calculated from that. Another source of error would be when finding the heights of the ramp and the diameter of the ball. Since the height of the ramp is found through measuring with a ruler, we are not a hundred percent sure exactly where the height lies which also affects the slope which in turn affects the C value. Use error propagation calculations (as appropriate) to support your explanation. The uncertainty is C for the filled ball is 0.032. For the hollow ball it is 0.020. For the mystery ball it is 0.040. Experiment Reflection The C value is the relationship of the moment of inertia and thus, we can find that the coefficient of the mr^2 of the mystery ball is 0.559 and then we have an equation for the moment of inertia of the mystery ball. I find it very interesting how we can use velocity and height to calculate moment of inertia of a ball by finding the coefficient that relates it to the mass and radius of the object. Labs like this show how much physics is related to the natural world around us and how everything else is related to. During class, we learn how to find the coefficients in front of mr^2 through integration and calculations but here, we are able to find it through experimentation. Additionally, again this lab shows how with more data we are able to have a very sample set. Because we used five different heights per ball, we were able to plot a more accurate graph, and thus have a more accurate C value, which leads us to a more accurate understanding of moment of inertia.
