Conservation of Momentum: Law, Formula & Real-Life Examples
Master the law of conservation of momentum — one of the most powerful principles in physics. Learn the formula, types of collisions, derivations, and real-world applications like rocket propulsion and car crashes.
What is Conservation of Momentum?
The **law of conservation of momentum** states that in a closed system (no external forces), the total momentum before an event equals the total momentum after the event.
Momentum is a vector quantity and is conserved in all collisions and explosions when external forces are negligible.
The Law of Conservation of Momentum
Total momentum before collision = Total momentum after collision
(When no external force acts on the system)
Momentum (p)
p = m × v
Unit: kg·m/s (vector quantity)
Types of Collisions
- Elastic Collision: Both momentum and kinetic energy are conserved
- Inelastic Collision: Momentum is conserved, but kinetic energy is not
- Perfectly Inelastic: Objects stick together after collision
Real-Life Examples
Rocket Propulsion
Rocket pushes gas backward (action), gas pushes rocket forward (reaction) → conservation of momentum.
Car Crash
In collisions, total momentum before = total momentum after (if we consider the system of both cars).
Billiard Balls
When one ball hits another, momentum is transferred while total momentum remains constant.
Ice Skater Pushing Another
Both skaters move in opposite directions to conserve total momentum.
Solved Practice Problems
Problem 1: A 2 kg ball moving at 5 m/s collides with a stationary 3 kg ball. After collision, the 2 kg ball stops. What is the velocity of the 3 kg ball? (Assume perfectly inelastic? No — use conservation)
Solution: 2×5 + 3×0 = 2×0 + 3×v → v = 10/3 ≈ 3.33 m/s
Problem 2: Explain why rockets can accelerate in space (vacuum) using conservation of momentum.
Answer: Rocket ejects gas backward, gaining forward momentum to keep total momentum zero.
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