My Math Forum Center of mass

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June 1st, 2013, 07:07 AM   #1
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Center of mass

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 June 4th, 2013, 02:11 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Center of mass The center of mass (since these are geometric figures and have no "density function", strictly speaking the term is "centroid") of a triangle is the average of the coordinates of the three vertices. For figures with more than three sides, you can divide into triangles, find the centroid and area of each, then do a "weighted average", the centroid of each triangle weighted by its area. Or you could use the integral definition of "centroid" $\overline{x}= \frac{\int\int x dydx}{\int\int dydx}$ $\overline{y}= \frac{\int\int y dydx}\int\int dydx}$ where the integrals are taken over the entire figure.

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