Finding Centroids and Moments of Inertia

by Russel Weich

Submitted : Fall 2009

For my 2009 Fall Calculus class final project, I have been given an object which consists of a semi-circle and a triangle connected at the origin along the y-axis. I was asked to find the Moments of Inertia for each object to ultimately get one equation evolving both objects as a whole with respect to the x and y axis's, which I learned and used very frequently in this year's Calculus class. I was also asked to provide the proper equations for the Centroids of each, which I will use in future engineering courses. By performing these tasks for the given object, I have seen how the equations are put into perspective for my future career in Civil Engineering. I have used many double integrals, as well as other valuable features from Calculus, to obtain the correct formulas. I have put them into very easy to read steps which would or could ultimately help someone to understand about both of these subjects if the need would arise. This project has provided me with new knowledge, as well as brought back information that maybe I had forgotten or was maybe not fully capable of doing before. It allowed me to explore these subjects more in depth and has added essentials to my tool box which I hope will assist me in the future in my professional engineering career.

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