How does the center of mass move when no external force acts on a system?

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When no external force acts on a system, the center of mass moves at a constant velocity in a straight line, consistent with the principle of inertia.1

In physics, the center of mass is the point in a system where the total mass can be considered concentrated. When a system is free from external forces, the internal forces exerted by the parts of the system on one another—which may cause the individual parts to accelerate—always cancel each other out due to Newton’s third law. Consequently, the total linear momentum of the system remains conserved. Because the momentum of the center of mass is equal to the sum of the momenta of all individual parts, the conservation of the system's total momentum dictates that the center of mass itself must maintain a constant state of motion.2314