Moment of Inertia PHYS-141

Survey

Before we start today's lab, we are asking all students to complete a short (<5 minute) survey in which you will have a chance to provide feedback on your TA. Your answers are anonymous and will not affect your grade in any way. You may access the survey from your personal computer, a lab computer, or your phone.

If you cannot or do not want to complete the survey now, you may complete it at home. The survey will remain open until Saturday, November 18 at 5:00 pm.

Introduction


For your final PHYS141 lab you will do a straightforward moments of inertia measurement. You will measure the moment of inertia of the iOLab device about its long axis using two different methods. You will then compare the results of both measurements to the value which you get from calculating what the moment of inertia should be for a simple rectangular object. We don't however expect this calculation to be accurate as it assumes a uniform mass distribution through out the object. The iOLab device however is mostly empty space with concentrations of mass where the internal components reside. The motivation for performing the measurement two different ways is to establish how reliable your measured values are. If you get the same result using independent methods you have more confidence that your measurement is robust. If your two techniques yield different values, taking into account experimental uncertainties, then you have to do more investigation to understand what your experimental results mean.

This is an important and common theme in science.

Group Lab Notebook

Things which should make it into your group notebook include, but are not limited to:

  • Diagrams and photos showing important details of your setup.
  • Raw data, including measurements such as lengths and heights or values of masses used.
  • Estimates on uncertainties in measured quantities.
  • Screen shots of data recorded from the iOLab which illustrate how regions of interest were determined or which show interesting features in the data.
  • Results of calculations, plots and fits of data.
  • Enough verbal description of your process and procedures that you could come back into the lab a year from now and reproduce the experiment.

Pedagogy Note

There is no recipe for what should go into a lab notebook. No one can teach you how to do it before you go into the lab. There are broad and general guidelines like those given above, but every experiment and every scientist is different. Learning how to keep a good lab notebook is a lifelong process which is never perfect. You simply have to get in the habit of taking notes when doing experiments, and learning painful lessons when you end up having to go back and retake all of your data because the notes in your notebook were inadequate when it came time to writeup your work for publication.

Getting Started

Your experimental goal is to determine the moment of inertia of the iOLab device about its long axis.

mom-inertia-apparatus.jpg

The main components of your experimental apparatus are shown in the photograph above. You have an iOLab device, two wheels cut from a cardboard shipping tube, and a piece of wood with a smooth surface. The wheels can be fitted onto the iOLab device as shown in the photograph below.

rolling_iolab.jpg

Part 1 - Calculate the Moments of Inertia

Begin by calculating the moments of inertia for the iOLab and the wheels under the assumption that their mass distribution is even through out their bodies. Do a careful job of estimating the uncertainties and propagating them through the calculations. Later you will need to compare your measured moments of inertial with the calculated ones and assess their degree of agreement.

Treat the iOLab device as a rectangular object for this purpose. Note that the rounded corners, wheels and non-uniform mass distribution of the iOLab will cause this calculation to be inaccurate, this is the reason for determining it experimentally.

If you look closely at the wheels provided you will note that they were cut rather roughly out of a long cardboard shipping tube. The two edges of the wheels are likely not uniform and this will contribute to your uncertainty.

Part 2 - Dynamics Measurement of Moment of Inertia

One way to measure the Moment of Inertia of the system, where system refers to the combination of the iOLab with its attached wheels, is to begin with an analysis of the forces acting on the device when it rolls down an incline.

  • Work out the analysis of the forces involved to determine what data you will need for this measurement.
  • Devise and execute an experiment to use the sensors in the iOLab to perform the experiment.
  • Determine the basic uncertainty in your measured quantities considering only the measurement resolutions.
  • Consider the main uncertainties in the measured quantities. Note there are two potential sources of such measurement uncertainties; the inherent accuracy and precision of the measurement tools, systematic factors such as rolling friction, non-circular wheels, etc. For this lab we are not asking you, aside from the basic uncertainties as determined in the above bullet point, to investigate and correct for these factors. We just want you to come up with a list of what you feel are the most important limiting factors in how well you are able to measure the Moment of Inertia using this method.

Part 3 - Energetics Method for Measuring the Moment of Inertia

You can also approach this problem from a conservation of energy point of view.

  • Analyze the problem in terms of the conservative energy losses and gains as a way to find the Moment of Inertia of the system.
  • Figure out how to use the apparatus and the sensors in the iOLab device to perform this measurement.
  • Determine the basic uncertainty in your measured quantities considering only the measurement resolutions.
  • Consider the main systematic uncertainties in the measured quantities. Note that this will include possible sources of non-conserved energy losses. Again we are not asking you to investigate and correct for these factors. We just want you to come up with a list of what you feel are the most important limiting factors, aside from the basic uncertainties as determined in the above bullet point, in how well you are able to measure the Moment of Inertia using this method.

Assessment of Results

Use the calculated Moments of Inertia for the wheels and your data, determine the Moment of Inertia for the iOLab device for both the Dynamic and Energetic methods. Propagate your basic measurement uncertainties so that you have an uncertainty for both experimentally determined results.

Compare the three values you obtained for the Moment of Inertia of the iOLab device about its long axis.

  • How do your experimentally determined values compare with the one you calculated assuming uniform mass distribution within the iOLab device. Quantify the degree of agreement or disagreement,
  • How do your two experimentally determined values compare with each other? Again, quantify the degree of agreement or disagreement.
  • Given your assessment of the possible sources of systematic uncertainty in each method, which do you feel is more reliable?

Post Lab Assignment

For your post lab assignment summarize your conclusions regarding the actual Moment of Inertial of the iOLab device about its long axis, and the two methods used to measure it.

REMINDER: Your post-lab assignment is due 48 hours before your next meeting. Submit a single PDF on Canvas.

!! Congratulations !!

You have now completed the lab component of PHYS141.

Good luck on your final exam and have a great holiday break.