What you are looking at
Two pucks on a frictionless surface (no walls, no external forces). The gold × marks their
center of mass — the mass-weighted average position:
r_COM = (m₁r₁ + m₂r₂) / (m₁ + m₂)
The pucks collide, bounce, stick, or fly apart; the × ignores all of it and glides along its dashed straight
line at constant velocity.
Why internal forces can't move the COM
Differentiate the definition and you find the COM moves with the total momentum:
v_COM = (m₁v₁ + m₂v₂) / M = p_total / M
During a collision the bodies hammer each other — but by Newton's third law those forces are
equal and opposite, so their impulses cancel in the sum. Total momentum can't change, and
neither can v_COM. Only an
external force can accelerate the center of mass:
F_external = M·a_COM
Collisions, seen properly
Sticky or bouncy, gentle or violent — the collision redistributes momentum
between the bodies while
the total rides through untouched. Kinetic energy is another story (it survives only if e = 1), but momentum
conservation holds for every value of e. Watching the × is watching momentum conservation drawn as a line.
Explosions run the same law backwards
In explosion mode a moving body splits in two. The fragments' momenta relative to the COM must cancel
(m₁v₁' = −m₂v₂'), so the lighter fragment flies off faster — and the × never wavers from its straight path.
This is why the sparks of a bursting firework keep their centre gliding along the shell's original arc, and
why a rocket can accelerate only by
throwing mass out the back: pushing on your own pieces moves
the pieces, never the whole.
Things to try
Set e = 0 and watch the pucks stick — the merged blob moves at exactly v_COM, because it
is the
COM now. Make one mass much heavier and see the × hug the heavy puck. In explosion mode, compare fragment
speeds against the mass ratio: m₁v₁ = m₂v₂, always.