Moment of Inertia Pt. II
By now you should have a somewhat direct measurement of the I of your apparatus. Now you will measure this I more indirectly.
A. Notice the mass hanging from a string over the pulley. As it falls, it accelerates, and makes the apparatus spin faster. Derive an expression for the moment of inertia of your apparatus (ignoring the pulley) in terms of the mass of the hanging mass, the radius of the shaft, the linear acceleration of the hanging mass, and fundamental constants.
B. Now measure!!! You must measure…
i. the radius of the shaft. We have calipers and micrometers for this. Please do not use a ruler! And don’t forget the uncertainty in this measurement.
ii. the mass of the hanging mass (plus uncertainty!).
ii. the linear acceleration of the mass as it falls. It is up to you to figure out a good way to do this. Your result must have an uncertainty.
C. Compute the moment of inertia of your apparatus (with uncertainty!) based on your formula from part A and your measurements in part B. Is it the same as from your direct measurement?
The usual lab report will be required.
Name/Partners/Date/Title
Introduction – State the purpose of the experiment.
Theory – Include here your derivations of expressions for
a. the moment of inertia from your direct measurement.
b. the moment of inertia from B above.
Experiment – Say here what you did in order to take data. Pretend this document doesn’t exist, and include enough detail that someone 10 years from now could duplicate your experiment. Don’t forget equipment #’s, at least one diagram, and all of your data (radius of the shaft, mass of hanging mass, etc.). If you used a scale, you must mention which scale!
Analysis – Include your calculation of I from the direct measurement (with uncertainty), and your calculation of I from the linear acceleration of the hanging mass (the above, with uncertainty).
Discussion – Do your two I’s agree? Remember, they agree only if the ranges defined by their uncertainty limits overlap. If you get a result you did not expect, go back and check your work! If you made a mistake, go back and fix it, retaking data if necessary. Don’t turn in flawed results.
Conclusion – Repeat both I values (with uncertainty) and sum up why they did or did not agree. Nothing new should go in the conclusion.