1. The problem statement, all variables and given/known data A number of particles with masses m(1), m(2) , m(3),... are situated at the points with positions vectors r(1),r(2), r(3),... relative to an origin O. The center of mass G of the particles is defined to be the point of space with position vector R=m(1)r(1)+m(2)r(2)+m(3)r(3)/(m(1)+m(2)+m(3)) Show that if a different Origin O' were used , this definition would still place G at the same point of space 2. Relevant equations R=m(1)r(1)+m(2)r(2)+m(3)r(3)/(m(1)+m(2)+m(3)) Possibly C+R=R' 3. The attempt at a solution I think I need to translate R to a new coordinate system , which is O', and essentially show that If a vectors moves into a new coordinate system , calling constant c the distance between the new coordinate system and the old coordinate system, I have to show the magnitude of the vectors don't changed. So here it goes: R'=(m1)*(r1+c)+(m2)(r2+c)+(m3)(r3+c)/(m1+m2+m3)=m1r1+mc+m2r2+mc+m3r3+mc/(m1+m2+m3) C=R'-R=c(m1+m2+m3)/(m1+m2+m3)=c; Therefore, R=R'-C. Is that the procedure I would apply to proved That the magnitude of the vectors do not change at all as I move my position vectors into a new coordinate system?