Conservation of momentum · impulse · elastic & inelastic collisions · recoil · rocket propulsion
Fire a cannon and it kicks back; swing a Newton's cradle and the far ball leaps out; a rocket climbs on nothing but its own exhaust. In every closed system the total momentum — mass times velocity, added up with direction — is exactly the same before and after. That one idea, that momentum is conserved, explains collisions, recoil, and how anything moves through empty space.
This page covers the law of conservation of momentum — the total momentum of a closed system never changes — together with momentum (p = mv), impulse (F·t = Δp), elastic and inelastic collisions, recoil and rocket propulsion. By the end you'll be able to:
Every car crash, rocket launch, billiard break and rifle kick obeys it — and "Laws of Motion" is one of the most-tested chapters everywhere. We go beyond the syllabus, but we never skip it:
Searched as: law of conservation of momentum, p = mv, impulse, elastic and inelastic collisions, recoil, how rockets work.
Set the two masses and choose how the carts meet — bounce apart or stick together. Cart A rolls into a resting cart B; the total momentum bar holds steady while the speeds change. 🟢 real collision engine
Set the masses and pick bounce or stick to see what happens.
In plain terms: momentum is mass in motion — how hard something is to stop. In a collision the total momentum is simply shared out, never lost.
The momentum of an object is its mass times its velocity, p = mv, measured in kilogram-metres per second. It is a vector — it points the way the object moves — so a ball thrown left and the same ball thrown right have opposite momenta. Momentum measures how much motion something carries: a loaded truck rolling slowly can have far more momentum than a tennis ball whizzing past, which is exactly why the truck is so much harder to stop.
When two objects collide they push on each other with equal and opposite forces for the same time (Newton's third law), so each gains exactly as much momentum as the other loses. Add it all up and the total momentum is unchanged: whatever the system had before the collision, it has after. Two skaters who push off from rest drift apart with equal and opposite momenta, their total staying zero. This holds in a closed system — one with no outside push like friction or gravity tilting the result.
The playground above rolls cart A into a resting cart B. The Scene tab shows the carts and their velocity arrows before and after impact; the Momentum & energy tab shows that the total momentum bar is the same height before and after, while the kinetic-energy bars may differ. Choose Bounce (elastic) and the energy bar holds too; choose Stick (inelastic) and the energy bar drops as motion becomes heat — yet momentum is conserved either way. 🟡 maths of the picture
Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.
The physics is visible in the diagram; the maths usually hides. These little labs make it visible too — drag a slider and watch the momenta and arrows answer.
A few ideas about momentum are so common they feel obvious. Tap a card to flip it and bust the myth.
Lift and release one steel ball and it strikes the row; the momentum (and, because steel is nearly elastic, the kinetic energy too) passes cleanly through the still balls and launches the far one out at the same speed. One ball in, one ball out — the total momentum is conserved at every click.
A rocket hurls hot gas backward, so it must gain an equal and opposite momentum forward. It needs nothing to push against — no air, no ground — which is why it works in the vacuum of space. The more mass it throws, and the faster, the greater the thrust.
In a crash your momentum must fall to zero. Impulse (force × time) equals that change, so a longer stopping time means a smaller force. Airbags and crumple zones stretch the stop from milliseconds against hard metal to a gentler cushioned halt — and that is what saves you.
Once we could track momentum through every push and crash, we learned to fly by it, survive crashes with it, and pass it cleanly down a line.
Physics you can hold. Each project below demonstrates the law you just met — and the measuring is what turns a demo into a science-fair winner. Pick one, build it from things at home, and graph something.
Build: thread a straw on a long string, tape an inflated balloon to it, and let go — the air rushes back, the balloon races forward.
Measure: distance travelled vs balloon size (air expelled) — more mass thrown back means more forward momentum.
Build: hang five identical metal nuts in a row so they just touch; lift one end and release.
Measure: balls released vs balls that swing out — they always match, because momentum passes straight through.
Build: roll a marble down a grooved ruler into a stationary one (elastic), then into a blob of clay (inelastic).
Measure: speeds before and after with a phone slow-mo — momentum is conserved both times; the clay loses kinetic energy.
Build: sit on a skateboard and throw a heavy ball forward — you roll backward.
Measure: your roll-back speed vs the ball's mass and speed — heavier or faster throws push you back more.
Build: design a lander that lets an egg survive a drop using padding, springs or a parachute.
Measure: which design gives the longest stopping time — and so the smallest force — for the same fall.
Build: half-fill a bottle with water, pump in air and launch; the water blasts down, the bottle climbs.
Measure: launch height vs water volume — there is a best fill that throws back the most momentum per launch.
Momentum runs through every impact and every launch. Here are the questions that come up most — each answer reads on its own, lifted clean off the page.
The law of conservation of momentum states that in a closed system — one with no net external force — the total momentum stays constant: the total before any collision or explosion equals the total after. Momentum is mass times velocity (p = mv) and is a vector, so directions are added too. It follows directly from Newton's third law, and it holds even when kinetic energy is not conserved.
Momentum is the quantity of motion of an object, found by multiplying its mass by its velocity: p = mv. Its unit is the kilogram-metre per second (kg·m/s), and it is a vector pointing the way the object moves. A 1000 kg car at 20 m/s has 20000 kg·m/s of momentum, far more than a 1 kg ball at the same speed — which is why the heavy, fast object is so hard to stop.
| Feature | Elastic collision | Inelastic collision |
|---|---|---|
| Momentum | Conserved | Conserved |
| Kinetic energy | Conserved | Some lost to heat/sound |
| After impact | Bounce apart cleanly | May stick together |
| Example | Billiard balls | Clay hitting a wall |
Impulse is the change in momentum an object experiences: impulse = force × time = Δ(mv). A small force acting for a long time can give the same impulse as a large force acting briefly. This is why airbags and crumple zones save lives — they stretch out the time of a collision, so the same change in momentum needs a much smaller, gentler force.
A rocket throws hot exhaust gas backward at high speed. Because the system's total momentum must stay constant, the rocket gains an equal and opposite momentum forward. It needs nothing to push against — no air, no ground — so it works in the vacuum of space. The faster and the more mass it expels each second, the greater the forward thrust.
When a gun fires, it pushes the bullet forward and, by conservation of momentum, gains an equal and opposite momentum backward — the recoil or kick. Because the gun is far heavier than the bullet, it moves back much more slowly (m_gun × v_gun = m_bullet × v_bullet). The total momentum of gun plus bullet stays zero, just as it was before firing.
In a crash your momentum must drop to zero. Impulse (force × time) equals that change in momentum, so a longer stopping time means a smaller force. Airbags and crumple zones lengthen the time over which you stop — from a few milliseconds against hard metal to a longer cushioned halt — which sharply reduces the force on your body and prevents injury.
In a Newton's cradle, lifting and releasing one end ball sends it into the row. Momentum — and, because the steel balls are nearly elastic, kinetic energy too — passes cleanly through the still balls and launches the far ball out at the same speed. One ball in, one ball out, with the total momentum conserved at every click.
Conservation of momentum comes straight from Newton's third law. When two objects interact, they push on each other with equal and opposite forces for the same time, so they receive equal and opposite impulses. One object's gain in momentum exactly matches the other's loss, so the total momentum of the pair never changes — momentum conservation is the third law seen over the whole system.
Seven question formats, the way Beyond Dictionary serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Momentum is only ever borrowed — what one body gives up, another carries on.