Motion of COM

Motion of the center of mass is determined ONLY by EXTERNAL forces: M·a_COM = F_ext_net.

Internal forces (collisions, springs between parts, explosions) cannot change COM motion.

If F_ext = 0: V_COM = constant. System moves as a single particle.

Projectile that explodes mid-flight: COM continues parabolic trajectory until any fragment lands.

Two-body collision in absence of external force: COM moves with V_COM = (m₁v₁ + m₂v₂)/(m₁+m₂), unchanged by the collision.

Spring oscillation in a closed system: COM stays at rest; the two masses oscillate about it.

Earth-Moon system: Earth + Moon both orbit their COM (barycenter), which lies INSIDE the Earth (~4671 km from Earth's center).

Useful frame: COM frame — moves with V_COM. In this frame total momentum is zero; simpler for many problems.