The center of mass for a collection of particles is expressed as the mass-weighted average position of all the particles. Consider a two-particle system with known coordinates. The x-coordinate of the center of mass's position is the ratio of the sum of the product of the particles' masses and their respective position coordinates to the system's total mass. Similarly, expressions for other coordinates can be written. A time derivative of the position vector of the center of mass gives its velocity. The sum of the individual masses of the particles is the system's total mass. The product of the mass and velocity of individual particles gives a particle's momentum. So, the total mass times the center of mass velocity equals the system's total momentum. The rate of change of the system's total momentum gives the net force acting on the system. According to Newton's third law, the internal forces cancel out. So, the system's motion is dictated as if the net external force acts on the center of mass of the system.