blog 18

Last blog. 

The objective of this lab was to find the period of a semicircular pendulum rotated at its top and bottom.

We cut out a small semicircular disk of light material and measured its dimensions, then we rotated each around the two required orientations and measured the period.

In order to come up with a predicted value for period, we first had to find the moment of inertia around both axises. We did this by first finding the moment around its flat side axis, then using the parralel axis theorum to figure out its Icm. From I center of mass we could then use the parallel axis theorum again to find its moment of inertia of its curved side. Before all of this however, we had to integrate to determine the location of the center of mass.

After we had a value for each moment of inertia, we could calculate a theoretical period at small angles for each orientation by using T=I(alpha) calculations. All relevant calculations are as follows

As we can see, our predicted value around the curved axis was 0.707s, compared to the actual value of 0.72, and around the other axis 0.72s, compared to 0.722. Giving us an error margin of 1.9 and 1 percent off (respectively),  This small errors is probably due to some amount of friction in our pivot points, or the fact that this is an approximation assuming small angles, or some small measuring error when we found the dimensions of the pendulum.