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)

 

 

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 pre-drilled 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 rectangular-type 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.

 

 

 

 

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 T² vs D by opening 1-physicalpendulum.xls. Remember to save your group's copy as LastnameLastnameLastnamePhysicalPendulum.xls in your period's folder.

 

 

 

 

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

 

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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.