TEX document #10

In Stewart (and many other textbooks) the numerator M \overline{x} is denoted by M_{yz} in three-dimensional problems, and by M_{y} in two-dimensional problems. (The reason is that this quantity is the average of the displacement of the matter from the y-z plane or the y axis, respectively. Note that this notation is consistent with the one for moments of inertia, where I_{z} is the average of the square of the displacement from the z axis, for example.) Consequently, the formulas for the center of mass in two dimensions are

\overline{x} = \frac{M_{y}}{M} , \overline{y} = \frac{M_{x}}{M} .

These formulas strike some of us as illogical and confusing, which is why we avoid using them.