Calculation of Center of Gravity in Cylindrical Coordinates

by Amir Moussly

Submitted : Fall 2012

In this project, both parts of the problem are addressed using Excel spreadsheets. All calculations were made by creating formulae and translating them to Excel function language. The process is not difficult; in fact, it has proven beneficial to use Excel as the primary method of calculating area by step size radians. Part (a) allowed the luxury of using integration as a check equation. However, part (b) does not include a staple radius between data points and thus would make integrating checks exceedingly tedious. For this reason, Excel was the only medium used for calculations in part (b).

The conclusions were astounding. Part (a)’s result was very close to the check equation’s result, which proved the trapezoidal rule is a fairly accurate approach. Likewise, part (b)’s result was close to what was expected. It is interesting to observe the dichotomy between abstract mathematics and arithmetic. From the naked eye, you can visualize the result based on the graphs in the problem statement, and the level of accuracy of the results bridge the gap between imagination and logic. Using the trapezoidal rule via Excel is a powerful and effective method of finding the centroid of an arbitrary shape in polar coordinates.

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