Conservation of Momentum — Definition

Definition

Imagine you have a group of objects, say two billiard balls on a perfectly smooth table. If these balls collide, what happens to their motion? The principle of conservation of momentum helps us understand this.

It states that if there are no external forces pushing or pulling on this group of objects (like friction from the table or someone hitting them with a stick), then the total 'quantity of motion' of the group before the collision will be exactly the same as the total 'quantity of motion' after the collision.

This 'quantity of motion' is what we call momentum.

Momentum is a vector quantity, meaning it has both magnitude and direction. It's calculated by multiplying an object's mass ($m$) by its velocity ($v$), so $p = mv$. When we talk about a 'system' of objects, we mean all the objects involved in an interaction, like the two billiard balls.

An 'isolated system' is one where no forces from outside the system are acting on it. For example, if you consider the Earth and the Moon as a system, the gravitational force between them is an internal force.

If we ignore the Sun's gravity (an external force), then the total momentum of the Earth-Moon system would be conserved.

So, if ball A with momentum $p_A$ collides with ball B with momentum $p_B$, and no other forces are involved, the total momentum before the collision is $p_A + p_B$. After the collision, they might have new momenta, $p'_A$ and $p'_B$.

The conservation of momentum principle tells us that $p_A + p_B = p'_A + p'_B$. This holds true for any type of interaction, whether the objects bounce off each other (elastic collision), stick together (perfectly inelastic collision), or deform and move separately (inelastic collision).

It's a powerful tool for analyzing complex interactions without needing to know the intricate details of the forces during the interaction itself, as long as the system is isolated.