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How does the center of mass of an isolated system move?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

In an isolated system—one where no external forces act on the system as a whole—the center of mass moves at a constant velocity in a straight line, or it remains at rest.12

This behavior is a direct consequence of Newton’s laws of motion. While internal forces may cause the individual parts of the system to accelerate or change their individual momenta, Newton’s third law ensures that these internal forces always occur in equal and opposite pairs. Consequently, the sum of these internal forces is zero, meaning the total momentum of the system is conserved.12

Because the momentum of the system is equivalent to the total mass concentrated at the center of mass moving with the center of mass's velocity, the conservation of total momentum dictates that the center of mass itself must maintain a constant velocity. This principle allows physicists to analyze complex systems by treating them as if their entire mass were concentrated at a single point.123