Equipment
Each lab group will need the following equipment:
 two vertical support stands with
one horizontal cross bar  one slotted rod
 a triple beam balance
 a meter stick
 a LabPro
 a motion detector

diagram courtesy of Daniel Weaver (c/o 2008)

Background Information
This experiment is a simple exploration of the physical pendulum. We will start our investigation by using a “long rod” as our model. During the experiment, you will be using a metal rod with predrilled holes. Recall that the moment of inertia of a long "thin" rod about its center of mass is If we were being precise in our physical model the equation for a rectangulartype rod would be more appropriate. The moment of inertia for this more exact physical model is
where a represents the length of the rod and b is the rod's thickness.

Refer to the following information for the next three questions.
Physical Data: For your group's aluminum rod, measure a and b in cm and the rod's mass in grams.
Refer to the following information for the next three questions.
Comparing Moments: Calculate the rod's moment of inertia with each formula and compare your results.

I suspect that you will agree that in most cases where b << a, our first approximation, , will work just fine. From this point forward we use this simpler formula.
Data Collection The experiment is fairly simple. You need to measure the period of your physical pendulum for each pivot point above its center of mass, cm. I would recommend measuring either 5 or 10 full oscillations for small amplitudes less than 10º. As you complete your trials, fill out the following chart. Compute each period and measure each "Y" and "D" value to three decimal places.
Now we will use EXCEL to plot T^{2} vs D by opening 1physicalpendulum.xls. Remember to save your group's copy as LastnameLastnameLastnamePhysicalPendulum.xls in your period's folder.


Analysis and Conclusions
The classic expression for the period of a physical pendulum is .
For our apparatus the distance above the pivot point was called "Y" and the distance from the pivot point to the center of mass was called "D." Therefore we can express the formula for the period of our physical pendulum as where the parallel axis theorem helps us calculate
.
In our experiment we used a constantly changing axis of rotation which meant that the moment of inertia of our rod was also constantly changing. 
Refer to the following information for the next question.
Use the parallel axis theorem, , the moment of inertia of a thin rod about its center of mass, and the period of a physical pendulum given above to prove that the period of a physical pendulum that is pivoted a distance “D” away from its center of mass is given by:
Refer to the following information for the next three questions.
Now square both sides of the expression you derived above to get an expression for T^{2}, the yaxis value on your EXCEL graph.

Each group's lab report should include a cover page, a copy of your data table (with its highlighted row), and a wellannotated copy of your EXCEL graph showing all required calculations.
This lab is used with the permission of its designer:
David Jones
Miami Palmetto High School
Seminole Community AP Physics Institute
July, 2005