The Law of Conservation of Momentum
Simple Explanation
The law of conservation of momentum says that in any collision or interaction, as long as no external force acts, the total momentum of a system before the event equals the total momentum after it — momentum can be transferred between objects, but the total never changes.
Why Do We Need It?
This law lets you predict the outcome of a collision (like two colliding trolleys, or a gun recoiling when fired) without needing to know the details of the force during the collision itself — it follows directly from Newton's third law.
Worked Example
Find the velocity after a collision
A 4 kg trolley moving at 6 m/s collides with a stationary 2 kg trolley, and they stick together. Find their common velocity after the collision.
Why Does This Work?
During a collision, the two objects exert equal and opposite forces on each other (Newton's third law), for exactly the same time — so the impulse (and hence the momentum change) each object experiences is equal and opposite, meaning the total momentum of the whole system stays unchanged.
Real-Life Example
Rifle recoil
A rifle is fired: the bullet shoots forward, and the rifle kicks backward into the shooter's shoulder.
Before firing, the total momentum (rifle + bullet) is zero; after firing, the bullet's forward momentum must be exactly balanced by the rifle's backward momentum, so the total remains zero — this is why the rifle recoils.
Practice
A 5 kg trolley moving at 4 m/s collides with a stationary 3 kg trolley and they stick together. Find their common velocity after the collision. (Round to 2 decimal places.)
HardCommon mistake
Forgetting that momentum is a vector — in a head-on collision, velocities in opposite directions must be given opposite signs before adding the momenta together, or the total will be wrong.
Quick Review
- Total momentum before = total momentum after, when no external force acts.
- This follows directly from Newton's third law.
- Momentum is a vector — always account for direction with signs.