Table of Contents
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 23 at 5:00 pm.
Introduction
For your final PHYS141 lab you will do a 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.
Learning goals for this lab include:
- Applying physics principles learned in lecture to design experiments.
- Experimental design and verification.
- Testing underlying assumptions.
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.
If you need a refresher on how to use the iOLab you can access the tutorial from last week here.
Getting Started
Your experimental goal is to determine the moment of inertia of the iOLab device about its long axis.
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.
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.
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. 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.
For your post lab assignment you need to:
- Show your calculations for the moments of inertia of the hoops and the iOLab. Include propagation of the uncertainties in your measured quantities. [DA]
- Include your measured values for the moments of inertia calculation, along with uncertainties and proper units. Be sure to present them in a manner which is clear for the reader. Separate the data from the text and use tables where appropriate. [DA] [SC]
- For each of the measurement techniques include the following:
- Describe the relevant physics and provide a derivation of the relationship you will be using as the basis of your measurement. [SC]
- Describe, using photos and diagrams as necessary, the your experimental procedure for the measurement. Define your measured quantities and the source of their uncertainties. [EP] [SC]
- Include your data for the measurement. Use plots from the iOLab software, tables, etc. as appropriate. [DA]
- Show your calculation of the moment of inertia, including propagation of uncertainties. [DA]
- Summarize your final results for both methods. Include comparisons of the calculated and measured values for the moment of inertia of the iOLab about its long axis using your final values with uncertainties. [SC] [DC]
REMINDER: Your post-lab assignment is due 48 hours after lab. 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.