2 December 2014: Period and Moment of Inertia Lab 21

Objective:
The purpose of this lab is to be able to find the moment of inertia of a real life ordinary semicircle and use it to its period.

Procedure and Results:

The first thing to do is to cut out a semi circle out of a piece of cardboard. Some semicircles were drawn using a compass but ours was made using a protractor. It is important to note that you can not cut out a circle and then cut it in half; it has to be a semicircle.

The next thing to do was to to tape little hangers to each side of the semicircle. It is important to make sure the holes of the hangers are as close to the edge as possible as the later calculated moment of inertia is along the edge and not further out.

Next, we predicted the period we believed the semicircle would have. We did this by first calculating the moment of inertia of the semicircle and then relating it to period. Our calculations can be seen below:

As you can see from the picture, we calculated our period to be 0.636 s.

Next, we wanted to test the validity of our prediction so we set out to measure the semicircle's period.

We hung the semicircle we cut out by the hangers we had attached to a rod secured to a ring stand by clamps. On the same ring stand was attached a photogate with the use of more rods and clamps.The photogate recorded the oscillations of the semicircle and the data was saved to Logger Pro.








The recorded period was:

Our predicted period was .636 and its actual period was .611. Clearly they were not the same value so to find out by how much we were off we found percent error. Percent error can be found by:

So, our percent error was 3.93%

Conclusions:
We do not really know exactly why our calculations did not fall within the expected one or two percent error. We believe our calculations and our approach is correct and yet we still did not get the correct value. We believe that the source of error lies in the handling of the semicircle. We cut the semicircle a few days before we actually measured its period. We think during that time, the semicircle was bent and damaged causing its period to be distorted. Even though it did not meet the expected percent error, it is still amazing that we are able to find the period of a real life object cut by our own design with a percent error of <5%.