3) When an object oscillates, the period is dependent on the moment of inertia and the center of mass. We will prove with different objects that each period will come with a resultant differently. I will present first a theoretical approach for each object and later show the results of our experimental.
The objects we will be using in this lab will be a circular ring, and semicircle, and a isosceles triangle. I will present each each picture in order of the objects.
For this circular ring, I have to find the average moment of inertia between the outer and inner ring.
For the semicircle, we chose two points of the circle for the object to oscillate. The hemisphere of the circle and the top curvature of the circle. On the hemisphere, we know the moment of the inertia of the disk is still half times the mass and radius. To find the top curvature part of the circle of the moment of inertia, we applied the parallel axis theorem.
Lastly we did the isosceles triangle upright and upside down. The point of the triangle standing upright will be the apex and the middle of the base of the triangle will be called the base. We chose those two points to find the oscillation period of the object.
These two illustrations indicate the points of the moment of inertia. we found the moment of inertia at the apex, center of mass, and the base.
These are the results of the period for the object.
4) What we did for the experiment was to use logger pro oscillating sensor and detect the period of the objects. Here are the results of each object in the same order I presented in the theoretical results.
Object of the ring
Object of half circle rotated at the flat side
Object of the half circle rotated at the curvature side
Object of the triangle at the base
Object of the triangle at the apex.
Here is the summary results of the experimental results
5) Our experiment and theoretical results came close to what we predicted. Our margin error was on average 5% but it's really close. Applying the tape and paperclip for the object to oscillate was maybe was caused the error in our calculations or our measurements as well.
