The Physical Pendulum

Purpose: The purpose of the lab was to use the moment of inertia of two different shapes in order to try and predict their period.

Procedure: In order to  predict the period we needed to find the torque that the from the pivot point that was acting on the physical pendulums. Using the function Torque = Moment of Inertia * Angular Acceleration we are able to acquire a function for the system taking into account that they are small oscillations. We did this for a semi circle pivoted at the base in the middle and at the tip in the middle. The same thing was done for a triangle that was pinned at one of its sides and in the middle of one of the sides. The triangle was isosceles.

The picture below shows the semi circle we used. The material used to make it was Styrofoam.

The triangle we used is in the picture below.

Data: The data used were the measurements of the circle and triangle.

The graph below is that of the circle when it was at its base. The period we got for this one was 0.5994 s.

The table below shows the period of the top (curved side) of the semi circle. The period of this side was 0.5991 s.

The period of one of the sides of the triangle is shown below.

Calculations: In order to find the period we needed to find the center of mass of both of the semi circle and the triangle and then use the parallel axis theorem and get the moment of inertia at the pivot we choose. Then we could find the torque and get a period of the pendulum after that.

The picture below shows how we got the center of mass of the semi circle.

The picture below shows we got the moment of inertia of the semi circle.

The picture below shows we came to get the period of the whole system.

The picture below the percent error of both the positions of the semi circle.

The picture below shows how we got the moment of inertia of the triangle and the period of it on one side. It came out to be 0.77 s.

The same thing was done to the one in the picture below.

 Summary: Overall the lab was successful because the percent error from the actual value was not off. The percent error for all trials were below 1%. Therefore we can come to the conclusion that the calculations to find the period are very accurate.