Boas Mathematical physics book, definition of center of mass

fluidistic

In Boas' book I can read that the definition of center of mass of a body has coordinates [itex]x_{CM}= \int x_{CM}dM= \int x dM[/itex].
Shouldn't it be this same integral but divided by M?!
Also, I didn't find the definition of center of mass for particles or any non continuous bodies.
I'd be grateful if someone could point me what I'm missing.

Edit: I forgot to say it's on page 210 in the 2nd edition.

WiFO215

How could this be true? The second equality is correct. Since x_CM is a constant, you can pull it out of your integral. There's your missing M. You'll thus have x_CM = integral(stuff)/M

For discrete objects, it is just a weighted mean of the positions. Should be in there somewhere!

fluidistic

My bad, I misunderstood the book. The first equality is wrong and the second is right as you said. Now I get it. Thanks a lot.
Yeah I know how to calculate the center of mass of discrete objects. I just wanted to be sure and refered to the book but couldn't find it (still didn't find it).

WiFO215

If that is so, then simply substitute in the density of the object delta functions for those mass points and the continuous reduces to the discrete ;)