# Data Analysis

Part 1: Rolling Cylinder

From the theoretical section of this experiment we know that the angular velocity of a point charge can be described as:

But if the object is not a point charge then the angular velocity can be described as:

Using the data collected in the experiment decide which of these equations better fits your experimental data.

Deliverable #7: Justify your choice of model for the angular velocity for the tube rolling down the ramp.

Deliverable #8: Create a plot of angular velocity versus time for each of the ramp angles tested. Extract the slope of this data and compare it to the constants in the above equations. Create a plot of the slope versus the angle of the ramp.

Deliverable #9: Determine a numerical value for the moment of interia of the tube. Calculate the percent error from the moment of inertia of a hollow tube with the same dimensions. What could cause this difference.

Part 2: Falling Rod

Note: You are provided an Excel sheet for part of this analysis but you are allowed to convert the analysis performed in the spreadsheet into Python (or other language) code. If you do this you must submit the code with your other deliverables.

Deliverable #10: If you did not get the velocities from the experimental section, calculate those now. Create a graph of the x and y position of the rod versus time and a graph of the x and y velocity versus time.

Deliverable #11: Create a graph of the angular velocity of the rod versus time.

Deliverable #12: Determine the tangential velocity of the center of mass of the rod and the end of the rod from the experimental data. Compare these values to those you derive using energy consevation in the theoretical part of this experiment.

Deliverable #13: Download the spreadsheet located here and input your rod's properties and the initial conditions. Use the equations provided to iteratively fill out the Excel sheet. Let the Excel sheet autocomplete until the angle is 90 degrees. Write a paragraph or two explaining the iterative equations the Excel sheet is using.

Deliverable # 14: Get the angular velocity from the line on the spreadsheet where the angle is 90 degrees and compare it to the actual angular velocity (from the energy conservation) and from the experimental values. Discuss how these three values compare.

Deliverable #15: Create a plot of time versus angular velocity for your spreadsheet data and experimental data. Add a percent error score to the graph.