Now we introduce an important concept that often allows us to think of a collection of particles in terms of a single vector. Take for example a baseball. We don't really want to think of atom 1029890123890 being at position (1.112323,-2.21334123,0.123340984)cm and atom 1029890123891 being at position (1.112324,-2.21334122,0.123340985)cm etc.. It would take a long time to describe that baseball. We have the feeling that there is a simpler way to describe the baseball. It's got a radius and a mass, and a center coordinate. What we'll see now, is that the proper center coordinate to use for a ball, or any system of particles is the center of mass.
Let's start with two particles, a mass 
at position 
and
and position 
. The total mass 
. The
center of mass 
is defined as
For N masses, using summation notation we can write
