Center of Mass
Definition
The single point where an object's entire mass can be considered concentrated for analyzing its overall motion.
Symbol: · Unit: m (position)
Technical definition
The mass-weighted average position of a system: R = (Σ mᵢrᵢ) / (Σ mᵢ). The center of mass of an isolated system moves with constant velocity, and it follows the same trajectory a point mass would under the net external force.
Example
A thrown hammer tumbles wildly, but its center of mass traces a smooth parabola — exactly the trajectory of a simple projectile.
Common confusion
The center of mass is not always inside the object. A boomerang's or a donut's center of mass lies in empty space. It is a mathematical balance point, not a physical chunk of material.