Center of mass

The position given by the mass-weighted average of a system’s parts. Its motion follows from the system’s total mass and net external force, regardless of internal forces.

Center-of-mass frame: A reference frame whose origin moves with a system’s center of mass. In this frame, the system’s overall translation is removed, exposing its internal motion.
Mass: A physical property measuring inertia and, in Newtonian physics, the amount of matter in an object. Mass supplies the weights that determine each part’s contribution to the system’s position.
Elastic collision: A collision in which total kinetic energy and total momentum are conserved. The center-of-mass frame makes the before-and-after velocities in an elastic collision especially simple.
Geometric centroid: The geometric center of a shape, defined by averaging its points without regard to material density. It matches the center of mass only when the body's mass distribution is uniform.
Newton's laws of motion: Three laws relating motion, inertia, and forces in classical mechanics. The net external force determines center-of-mass acceleration through the system’s total mass.
Position vector: A vector specifying an object's location relative to a chosen origin. The center of mass averages the position vectors of the system’s parts.
Ballistic trajectory: The path of an object moving under gravity after launch, neglecting or simplifying air resistance. A thrown object’s center of mass follows a projectile path even as the object rotates.
Moment of inertia: A measure of how a body's mass is distributed relative to a specified axis. The center of mass locates translational motion; moment of inertia characterizes resistance to rotation.
Momentum: A vector quantity equal to an object's mass multiplied by its velocity. A system’s total momentum equals its total mass times its center-of-mass velocity.
Weighted average: An average in which each value contributes in proportion to an assigned weight. The center-of-mass formula is a weighted average with each part’s mass as its weight.

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