Newton's Cradle: Momentum & Energy Conservation (2D)
A 2D companion to the 3D cradle: each ball is integrated as its own pendulum under gravity, and an end-to-end collision rule shows why momentum and kinetic energy conservation together allow only one ball to swing out at a time.
This 2D companion drives the same per-ball pendulum equations and end-to-end collision rule as the 3D cradle, viewed from the side on a plain canvas: each ball swings as θ'' = -(g/L)sin(θ), and when an end ball crosses vertical moving inward its angular velocity is handed to the ball at the opposite end while every ball between them is reset to rest — the same rule that keeps a real Newton's cradle looking almost magical.
2D Newton's cradle: numerically integrated pendulum per ball, with a collision rule that transfers momentum and kinetic energy end-to-end. Adjustable ball count, pull-back angle, gravity and damping.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install
Momentum (mv) and kinetic energy (½mv²) must both be conserved in the collision chain. With equal masses, transferring the incoming velocity to a single outgoing ball satisfies both equations at once; splitting it across two balls would conserve momentum but not energy, so it never happens with matched steel spheres.
Air resistance and small inelastic losses at each contact bleed off a little kinetic energy every swing. This simulation models that with a damping slider; set it to 0% for a lossless, indefinitely-swinging cradle.
It sets how far the end ball is raised before release, which sets its initial potential energy and therefore the impact speed and swing amplitude that gets transferred through the chain.