# How to Locate the Center of Gravity

by siukwok
Tags: gravity, locate
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,569 Yes, saying that an object is "homogeneous" means it made of the same material throughout so, in particular, the density is constant. if the objecft is not homogeneously but the density varies continuously, and the geometry of the figure is reasonably simple, you can try integrating the density to find the mass: $M= \int\int\int_V \rho dV$ where $\rho$ is the density funcdtion. Then the x, y, and z coordinates of the center of mass are given by $$\overline{x}= \int\int\int x\rho dV/M$$ $$\overline{y}= \int\int\int y\rho dV/M$$ $$\overline{z}= \int\int\int z\rho dV/M$$ If the the object can be divided into several pieces, each being uniform, you can find the center of mass of each piece then form a "weighted" average of the coordinates, weighted by the mass of each piece.