⚡ Newton's Cradle
Lift balls on one side — the same number swing out the other side! Momentum is always conserved.
Lift balls on one side — the same number swing out the other side! Momentum is always conserved.
This interactive Newton's cradle demonstrates how momentum and kinetic energy travel through a line of identical hanging balls. Each ball is modelled as a simple pendulum and integrated with the small-angle approximation, while collisions are resolved by swapping the velocities of touching neighbours — the exact result for an elastic collision between equal masses. Lift one ball and exactly one swings out; lift two and two respond. It is a vivid, hands-on way to see conservation of momentum and energy at work.
A row of 3 to 7 equal-mass balls on strings. Each swings as a pendulum (angular acceleration proportional to −sin θ over the string length), and when two balls touch their velocities are exchanged. Because the masses are equal and the collisions are treated as elastic, both total momentum (p = m·v) and kinetic energy are preserved, so N balls lifted means N balls fly out.
Use the "Lift Left" buttons to raise 1–4 balls on the left, or "Lift Right" to raise 1–2 on the right, or "↔ Both" to launch from both ends. Sliders set the number of balls (3–7), the damping (0–50%, energy loss per swing), and the string length (80–180). "↺ Reset" restores rest, the counter tracks collisions, and you can drag any ball with the mouse or touch to launch it.
The cradle only behaves so cleanly because every ball has the same mass. When equal masses collide elastically head-on, they simply trade velocities, which is why the impulse passes straight through the stationary middle balls and emerges at the far end.
A Newton's cradle is a device of several identical balls suspended in a row so they just touch. When you lift and release a ball at one end, it strikes the line and an equal number of balls swings out the far end. It is a classic demonstration of the conservation of momentum and kinetic energy.
Both momentum (p = m·v) and kinetic energy must be conserved in an elastic collision. With equal masses the only solution that satisfies both rules at once is for one incoming ball to stop and one outgoing ball to leave at the same speed. So two lifted balls send two out, never one moving twice as fast.
The Lift buttons raise a chosen number of balls (1–4 on the left, 1–2 on the right, or both ends) to a fixed 45° angle and release them. The Balls slider sets how many balls hang in the row (3–7), the Damping slider adds energy loss per swing (0–50%), and the String Length slider (80–180) changes how slowly the pendulums swing.
It captures the key ideas well: pendulum motion under gravity and the velocity exchange of equal-mass elastic collisions. It is a simplified two-dimensional model, however — it uses the small-angle pendulum approximation, treats every contact as perfectly elastic, and ignores the elastic compression waves and tiny energy losses that occur in a real cradle.
No collision is perfectly elastic, so a little energy is lost to sound, heat and air resistance with each swing. Over time the balls slow and begin to move together rather than cleanly trading places. You can mimic this here by raising the Damping slider, which removes a small fraction of energy on every swing.