Physics · Mechanics

Conservation of Momentum

Simulation loading

Open Model Lab is preparing the live lab, controls, and graph surface for this concept.

Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: CollisionsReal collisions

Key takeaway

Momentum conservation applies to the whole isolated system. On the momentum graph, that means the total line stays flat even when the cart lines change.
Internal forces come in equal-and-opposite pairs, so they give the carts equal-and-opposite momentum changes without changing the system total.

Common misconception

If two carts push on each other, one of them can win more of the system momentum by pushing harder or by having more mass.

Inside an isolated system, the force pair is equal and opposite, so the momentum changes are equal and opposite too. The system total does not have a winner.

Keep momentum reasoning moving

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Real collisionsMechanics

Collisions

Collide two carts on one honest track, keep total momentum in view, and see how elasticity, mass, and incoming speed shape the rebound or stick-together outcome.

Apply it to launchesMechanics

Projectile Motion

Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.

Review the pulse viewMechanics

Momentum and Impulse

Push one cart with a timed force pulse and watch momentum, impulse, and force-time area stay tied to the same motion, readouts, and graphs.

Stay with this concept

Review, test, or free-play here when you want one more same-concept pass.

More practice optionsReview on the bench · Worked examples

Practice optionReview on the benchReplay the guided setup with the key controls and graphs in sight.
Practice optionWorked examplesCompare against solved walkthroughs after you try the setup yourself.
Practice optionFree play on the benchExperiment freely with the live controls before moving to another concept.

Reference and support

Use these calmer sections when you want a fuller explanation, examples, or accessibility support after the guided flow.

Return here when you want the slower reference pass.

Open reference and support

Equation snapshotMomentum of one object · Total momentumShow 2 equations

Momentum of one object
$p = m v$
One cart's momentum depends on both its mass and its velocity.
Total momentum
$p_{tot} = p_{A} + p_{B}$
Add the cart momenta to get the system total. In this one-dimensional lab, the sign shows direction.

Why it behaves this way

Explanation

Conservation of momentum is about the total momentum of a system, not about each object keeping its own momentum. If no external impulse acts on the two-cart system, the sum of the carts' momenta stays constant even while they push or pull on one another internally.

In this module, two carts interact on one track during one internal-force window. Change the masses, system drift, force, or interaction time, then compare the stage with the force graph, momentum graph, and center-of-mass marker. The cart momenta can redistribute, but the system total and center-of-mass motion should stay consistent.

Key ideas

01Momentum conservation applies to the whole isolated system. On the momentum graph, that means the total line stays flat even when the cart lines change.

02Internal forces come in equal-and-opposite pairs, so they give the carts equal-and-opposite momentum changes without changing the system total.

03Equal momentum changes do not imply equal speed changes. The lighter cart usually changes speed more because

p = m v

Worked examples

Live conservation checks

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the live stage and graphs as evidence. First compute the system total momentum at the instant shown. Then use the current interaction to predict the final momentum split and compare that prediction with the momentum bars, force graph, and center-of-mass motion.

Supporter unlocks saved study tools, exact-state sharing, and the richer review surfaces that support this guided flow.

View plans

Example 1 of 2

Frozen valuesFrozen at 0.00

At $t = 0 s$ , what is the system's total momentum?

t

Time

0 s

p_{A}

Momentum of cart A

0 kg m/s

p_{B}

Momentum of cart B

0 kg m/s

1. Write the system total

Use

p_{tot} = p_{A} + p_{B}

for the same instant shown on the stage.

2. Substitute the live momenta

p_{tot} = 0 + 0

3. Add them

p_{tot} = 0 kg m/s

System total momentum

p_{tot} = 0 kg m/s

The total momentum is essentially zero here, so the center of mass stays at rest even while the carts separate.

Quick test

Loading saved test state.

Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows two carts on one horizontal track with a fixed time window for an internal interaction. Each cart has a mass label, a velocity arrow, and optional force arrows that appear in equal and opposite directions during the interaction window.

Optional overlays can draw an isolated-system boundary around both carts, a center-of-mass marker, and centered momentum bars for cart A, cart B, and the system total. Changing the masses, system velocity, internal force, or interaction duration updates the carts, readouts, and linked graphs without changing the underlying track scale.

Graph summary

The force graph shows equal and opposite internal force lines during the interaction window plus a zero external-force baseline. The momentum graph shows the carts' individual momentum lines changing in opposite directions while the total line stays flat.

The velocity graph shows how the same momentum exchange can create different speed changes for different masses, while the center-of-mass speed stays constant for the whole isolated system.

Bench tools and share links

Keep stable concept links and exact-state sharing tucked away until you actually need to relaunch or share the bench.

Try this setup

Jump to a named bench state or copy the one you are looking at now. Shared links reopen the same controls, graph, overlays, and compare context.

Saved setups

Saved setups are a Supporter study tool. Stable concept links still work for everyone.

Checking saved setup access

Open Model Lab is resolving whether this bench can save locally, sync to an account, or open Supporter-only compare tools.

Copy current setup

Exact-state sharing is part of Supporter. Stable concept and section links still stay available.

Stable links

Progress and next steps

Keep progress signals, starter-track handoffs, and review prompts available without letting them compete with the live lesson flow.

Progress

Loading progress

Loading saved concept progress for this browser or synced account before showing completion status.