Why Area Can "Stand in" for Mass


We know that the center of mass of a system of n discrete objects is:

cm definition (1)

but suppose that we have divided some "homogeneous thin laminar plate" into sections and determined the center of mass of each piece. Now, mass density, rho, is given by:

rho = mass/volume


mass = density*Area*thickness

Substituting this into equation (1), and realizing the the density, rho, and thickness, t, of each piece are the same gives:

xbar = areas

so, if the continuous object is homogeneous and has a constant thickness, areas can "stand in" for masses when calculating centers of mass.


last update February 1, 2010 by JL Stanbrough