state the principle of conservation of momentum

Linear Momentum & Conservation

What is Linear Momentum?

Linear momentum is a measure of how much motion an object has. It depends on both the mass and the speed of the object.

Formula: $$\vec{p} = m\vec{v}$$
Where m is mass (kg) and v is velocity (m s⁻¹). The direction of p is the same as the direction of v.

Why is Momentum Important?

Momentum tells us how an object will behave when it collides with another. It helps predict the outcome of collisions, explosions, and many everyday situations.

Conservation of Momentum

The principle 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.

$$\displaystyle \sum \vec{p}_\text{initial} = \sum \vec{p}_\text{final}$$
This means that if two objects collide, the combined momentum of the pair stays the same, even though each object may change speed or direction.

Analogy: Ice Skaters Pushing Off

Imagine two ice skaters standing still on a frictionless rink. They push off each other and move apart.

- Before the push, total momentum = 0 (they're stationary). - After the push, each skater moves in opposite directions. - The momentum of one skater is exactly cancelled by the momentum of the other, keeping the total at 0.
This simple example shows how momentum is shared and conserved.

Examples & Practice

1. Two cars of equal mass collide head‑on at the same speed. What is their total momentum after the collision if they stick together?
2. A 0.5 kg ball is thrown at 10 m s⁻¹. What is its momentum?
3. During a rocket launch, the rocket ejects 1000 kg of exhaust at 300 m s⁻¹. If the rocket’s mass is 10 000 kg, what change in momentum does the rocket experience?

Quick Check: Momentum Table

Key Takeaway

In any isolated system, the total momentum stays the same before and after an event. This powerful rule helps us solve problems in collisions, explosions, and even everyday sports like soccer ⚽️ or basketball 🏀.