Lab 17: Finding the moment of inertia of a uniform triangle about its center of mass

Lab 17: Finding the moment of inertia of a uniform triangle about its center of mass

Authors: Lab conducted by Mohammed Karim (author), Bemaya, and Loius.

Objective: Compare theoretical and experimental values of moments of inertia.

Theory/Intro: Using the parallel axis theorem, we can calculate inertia of the triangle at a certain point. In this experiment, we will find the moment of inertia of the pulley system alone, then attach the triangle, and measure it again. By subtracting the two moments of inertia, we can calculate the triangle alone and compare the results.

Apparatus/Procedure:

               Like lab 16, we are using the same mass-pulley system. First, we attached a mass and measured the average angular acceleration using LoggerPro. The value for the “empty” system was 2.186 rad/s^2. Next, we found the value for the triangle with the longer side up, as 2.0205 rad/s^2. Lastly, the value for the triangle with the longer side down, was 1.8375 rad/s^2. Using angular acceleration, we could calculate the experimental values for inertia. We then calculated the inertia through the parallel axis theorem (See Figure 17.1) and compared the results.

Data Tables:

Figure 17.1 - Calculations

Figure 17. 2 - Angular Acceleration Empty

Figure 17.3 - Angular Acceleration Triangle Up

Empty: 0.000278 kgm^2 (experimental)

Triangle up: 0.000236 kgm^2 (experimental), 0.0002444 kgm^2 (theoretical)

Triangle down: 0.0005374 kgm^2 (experimental), 0.0005672 kgm^2 (theoretical)

Analysis: The data shows the calculations behind finding the inertias of certain objects. Using the parallel axis theorem, we were able to find the theoretical data. By subtracting the empty pulley with the triangle pulley, we were able to find the inertia of the respective shape.  

Conclusion: This experiment expected us to get close values between our experimental and theoretical values. Our results are close; however, we are off by a small value. This could be primarily due to the uncertainty of the forces applied. There could have been little friction in one run and more friction in another. Also, there are many uncertainties relating to our calculations such as rounding and measuring errors, and we may have neglected factors such as friction and varying acceleration. As acceleration was not constant, we simply averaged it, which could have led to more uncertainty depending on the discrepancy of our values.