the same origin. The symbol ∑

the same origin. The symbol ∑ (the Greek letter sigma) denotes summation, in this case over n particles. The sum is the total mass of the system. Suppose that we have three particles, not lying in a straight line. We may define x– and y – axes in the plane in which the particles lie and represent the positions of the three particles by coordinates ( x , y ), ( x , y ) and ( x , y ) respectively. Let the masses of the three particles be m , m and m respectively. The centre of mass C of the system of the three particles is defined and located by the coordinates ( X, Y) given by X ( .3a) m y m y m y Y ( .3b) For the particles of equal mass m = m = m = m , X m y Y Thus, for three particles of equal mass, the centre of mass coincides with the centroid of the triangle formed by the particles. Results of Eqs. ( .3a) and ( .3b) are generalised easily to a system of n particles, not necessarily lying in a plane, but distributed in space. The centre of mass of such a system is at ( X, Y, Z ), where X