Finding the Moment of inertia of a uniform triangle: Jose Rodriguez: Lab Partners: Kevin Tran; Kevin Nguyen: lab completed 5/22/17

The purpose of this lab was to determine the moment of inertia of a right triangular thin plate around its center mass, for two perpendicular orientations of the triangle.

To achieve this experiment we used an apparatus in combination with Logger-pro that allowed us to measure the system's angular acceleration, made some measurements, and used the parallel axis theorem in order to easily calculate the inertia of the triangle around its center of mass.  For instance, we used force equations to derive a formula for the inertia of the system in combination with the given angular acceleration from the graph of Logger-pro and then calculated the inertia with the parallel axis theorem easily.  Then, with the differences in the trials of the calculated inertia per trial we were able to obtain a quantity for the inertia value of the triangle upright and sideways.

First, we set-up the apparatus and measured the triangles dimensions before we hooked up Logger-pro to begin the first trial of just the apparatus spinning.  Next, we made sure to record the data for the angular acceleration during decent and ascent for further calculations and proceeded to complete the next two trials with the change in the direction of the triangle making sure to record the acceleration values as well.  Last, from our calculated inertia quantity per trial we calculated the difference and recorded those values for the triangle's inertia in the two directions.

Image #1) This image illustrates the dimensions of the triangle.

Image #2) This image shows the calculations for the inertia of the triangle around one edge and the inertia around the center of mass.

Image #3) This is the calculation for the center of mass of the triangle.

Image #4) These are the calculations for the inertia of the system starting with just the system, and then the triangle upright followed by sideways.

Image #5) This is the apparatus that we used. Note, this is the set-up for the first trial of the system only.

Image #6) This image shows the setup for trial two when the triangle was upright.

Image #7) This image shows the graph that we got from logger-pro which gives us the angular acceleration on the way up and down.

Image #8) This image shows the graph for trial two when the triangle was upright.  Note that the slope of the graph is the angular acceleration value because it is an omega vs. time graph.

Image #9) This is an image of the final calculations for the moment of inertia for the triangle in the respectively drawn position. Note that the moment of inertia for a horizontal triangle is larger than the vertical one.

In conclusion, we did seem to find the inertia values for the three trials for the system.  The inertia for the triangle itself is seen in image #9 and it shows that one was a larger value than the other.  As for errors in the experiment, there was probably some frictional force involved that interfered and altered the data but regardless I think the horizontal spin would still be larger.  Also, air resistance might have applied some force on the experiment as well.  Lastly, I think the inertia for the horizontal triangle was larger because the radius of the rotation was larger while the mass stayed constant.