Lab 19: Moment of Inertia of a Right Triangle

Partners: Chong and Aiqi

Theory/Introduction:

The purpose of this lab is to determine the moment of inertia of a right triangular thin plate around it’s center of mass for two perpendicular orientations of the triangle.

We will be determining the Inertia using an experimental method and a theoretical method, then compare the results. The theoretical way of calculating the inertia about the rotation around the center of mass is by using the parallel axis theorem and solving for I_cm. We calculated the Inertia about the side of the triangle by making making small dI’s of the rotation of several small rods that made up the triangle then integrated them.  After finding the inertia around the edge we implemented the parallel axis theorem.

Our experimental approach involved taking the inertia of the disk system alone then taking the inertia of the disk-triangle system. Subtracting the disk system from the disk triangle system will give us the inertia of the triangle.

Experimental Procedure/Apparatus:

First we made sure to get the dimensions of the triangle along with the mass.

We mounted the triangle on a holder and  the upper disk. The upper disk floats on a cushion of air. A string is wrapped around the pulley on top of and attached to the disk and goes over freely-rotating “frictionless” pulley to a hanging mass. The tension in the string exerts a torque on the pulley-disk combination. By measuring the angular acceleration of the system we were able to determine the inertia of the system (just like our last lab).

Experiment 2

Experiment 1

We followed the same experimental procedure as the last lab to get our angular accelerations.

Analysis:

Here we took the average of the accelerations going up and down and plugged the values into our inertia equations (same equations from last lab):

Here is our theoretical vs. our experimental results:

Conclusion:

Overall our lab was a success. Our percent errors for each triangle were fairly close experiment 1 had 4.4% and experiment 2 was 2.5%. One of the systematic errors that helped cause this percent error was the fact that the disks rotation was not actually frictionless, this caused the experimental values to be lower than our calculated values. The experimental value was also lowered from the air drag caused by the triangle’s rotation. Even with these errors however, we were still able to get a good estimate of the inertia of the triangle along two different orientations.