Suppose we've arduously calculated the center of mass of a system
of 6 masses 
. And now we want to include another 3
. Do we have to redo the entire calculation? No!
A little mathematical manipulation should convince you that we
can the calculations of the center of masses of masses 1-6 and 7-9.
to calculate the center of mass of masses 1-9 . This is illustrated
pictorially:
{
Call the center of mass of 1-6 
. It has a total mass of
. Similarly call
the center of mass of 1-3 
. It has a total mass of
. Then what happens if we calculate the center of mass
of these two ``pseudo" particles? We get
By pluggin in the definitions of center of mass, you should be able see that you get quite a few cancellations and finally convince yourself that this is equal to
which is just the center of mass of the complete 9 mass system.
