PHYS4A/ Fall 2014; Periods of Oscillations

Purpose: The goal of the experiment was to calculate the moments of inertia for a triangle and a semi circle. These moments were then used to calculate a theoretical period of oscillation for both objects.

For this experiment, we had to cut a triangle and a semicircle out of a foam and calculate theoretical periods of oscillation under small angles and then relate that to experimental values found with loggerpro. Unfortunately, the triangle data was lost ( I really have no idea where it went) and I only have the semi circle data.

To start the prep for the experiment, we had to find the moment of inertia of the semicircle at the center of mass using calculus. By now, we have done these kinds of calculations many times and you should be able to follow the math below.

Once the moment of inertia at the center of mass was found, we then were able to once again use Newton's 2nd Law to find an angular acceleration of the object. This value was then related to the formula

(angular acceleration) = -(angular velocity)^2 * (displacement)

(alpha) = -(omega^2) * (theta)

Since all we had to look for was the constant before the displacement (theta) and relate that to the equation above, we could figure out an angular velocity value. This value was then used to calculate a period using the equation

(Period) = 2pi/angular velocity

T=2pi/(omega)

 From the calculations above, we were able to find a theoretical period value of 0.889s. We then went over to the setup and use loggerpro with a photogate that was able to record the period of the oscillations. From loggerpro, we got an experimental period of 0.640s. When compared to our theoretical value, we had a 7.72% error. This could be attributed to the pivot not being exactly center or the width of the hanging tape breaking the photogate being too large and recording shorter periods due to a sooner break in the light.

And this brings an end to the PHYS4A Fall 2014 Semester. Not too sure if Prof. Wolf did this on purpose but the final experiment was similar to the very first experiment we did with oscillations in a photogate.  The way we started was the way we ended but more knowledgeable about physics and how the world around us works.