Motion of COM
v_COM is constant when F_ext = 0 — see COM move in a straight line despite collisions.
Key Notes
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.
Formulas
COM acceleration
Total external force / total mass.
COM velocity from momenta
Mass-weighted velocity average.
Trajectory under constant F_ext
COM follows projectile motion regardless of internal dynamics.
Important Points
COM motion is THE KEY simplification of multi-body problems. Internal complexity doesn't matter for it.
Even an exploding bomb's COM keeps following the parabolic projectile path while the pieces fly off in all directions.
In a closed system (no external force), COM moves at constant velocity (or stays at rest).
Two-body system: COM frame eliminates total momentum. Collisions are easier to analyze there.
Earth-Moon barycenter is inside Earth ⇒ Earth wobbles, Moon orbits — both around the barycenter.
Common pitfall: thinking explosion 'kicks' the COM. It doesn't — only external forces can.
Motion of COM notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.