9.14: Significance of Center of Mass
The center of mass of an object is defined as the mass-weighted average position of all the particles that comprise the object. The significance of the center of mass of an object can be seen by looking at its dynamics. The time derivative of the center of mass gives its velocity, assuming that the object's mass remains constant over time. Furthermore, the total linear momentum of an object can be seen as the linear momentum of a single particle of the object's total mass moving with the velocity of the center of mass.
The forces acting on every particle of an object can include internal and external forces. Due to Newton's third law of motion, the internal force exerted by particle one on particle two will be equal and opposite to that of the force exerted by particle two on particle one. Thus, all the internal forces of an object cancel out. Therefore, the net force acting on an object is only the external force. The net external force on an object's motion can be viewed as if the net force is acting on the center of mass of the object. The center of mass of an object obeys Newton's second law of motion, such that the conservation of linear momentum of a system holds if no net force is acting on the object.