Bouncing Balls Physics: Momentum (2D)

World

Gravity 9.8 m/s²

Wall restitution 0.75

Collisions

Ball-ball elasticity (e) 0.90

Ball count 22

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Elapsed time

0.0 s

Kinetic energy

0.0 J

System |p|

0.00 kg·m/s

Collisions/s

How it works

Each disk has mass proportional to its area, m = k·r². Every ball-ball impact is resolved as a true impulse-based elastic collision along the contact normal n, not a velocity swap:

v_rel·n = (v2−v1)·n
j = −(1+e)·(v_rel·n) / (1/m1 + 1/m2)
v1' = v1 − j·n/m1
v2' = v2 + j·n/m2

Because the impulse j·n is applied equally and oppositely to both balls, total momentum m1·v1 + m2·v2 is conserved exactly by every ball-ball collision regardless of the elasticity slider — only kinetic energy depends on e (e=1 conserves it, e<1 dissipates some into "heat"). Gravity and wall bounces are external forces, so they change the system's total momentum over time — that part is physically correct, not a bug in the conservation law.

e = 1 — perfectly elastic ball-ball collisions (no kinetic-energy loss on impact).
e = 0 — perfectly inelastic along the contact normal (balls lose all relative normal velocity on contact).
Wall restitution — independent from ball-ball elasticity; controls how much speed each ball keeps after hitting the floor or a side wall.

Ball (color = speed) Bigger = more mass