Lab 17

Finding the moment of inertia of a uniform triangle about its center of mass.

Kyle Garibaldi
Partners: Sam Chen, John Valle
Date: 11-16-16

Goal:

We are determining the moment of inertia of a right triangle about its center of mass, for two orientations: upright and laying on it's side.

Summary:

The setup of this lab involves using the torque pulley device. (picture here)
We hang a weight from a string connected to the disk holding the triangle. The weight is pulled downwards by gravity, accelerating the disk and triangle system proportional to the moment of inertia of the triangle. We measure angular acceleration of the disk without the triangle and with the triangle to determine the difference. This difference is the moment of inertia of the triangle. We will compare and analyze this experimental moment of inertia to the theoretical moment of inertia and see if our theory holds true.

We need to have calculations prepared that will enable us to compare experimental I to theoretical I, shown below.

Procedure:

The experimental apparatus is set up as pictured below. We took appropriate measurements necessary in order to complete our calculations. We connected a computer/logger pro setup to the apparatus in order to measure angular speed of the disk. We graphed the data, and took the slope of the resultant line to get angular acceleration.

Apparatus setup with laying triangle

Graph of angular velocity vs. time,
slope is angular acceleration

radius of torque pulley: 0.027 m
hanging mass : 0.025 kg
triangle mass : 0.4536 kg
triangle height : 0.1463 m
triangle base : 0.098 m

Analysis:

With all our data combined, we form captain planet!

Experimental vs. Theoretical Inertia

Conclusion:

In regards to the upright triangle, our experimental and theoretical values are virtually identical. This indicates that we ran a effective experiment that matched our theoretical model. Regarding the laying triangle, our experimental and theoretical outcomes had a 9% difference which indicates we made some errors somewhere along the way, either in the form of data measurements or assumptions. The fact that one model had little to no error while the other had significant error is puzzling, and makes me think that perhaps the laying triangle measurements might be at fault.