How do you use conservation of momentum?

Momentum is defined as an object's mass multiplied by its velocity. The equation is $p = mv$, where $p$ is momentum, $m$ is mass, and $v$ is velocity. Because velocity has a direction, momentum is a vector. This means the direction an object travels is just as important as how fast it is going.

You can use this rule whenever a system is "isolated." This means there are no external forces pushing or pulling on the objects involved. During a quick collision on a slippery surface, we assume the forces the objects exert on each other are much larger than any outside forces like friction. Because the objects only act on one another, their total momentum stays constant.

To use conservation of momentum, you write an equation that says the total initial momentum equals the total final momentum: $p_{initial} = p_{final}$. For two objects colliding, you expand this to $m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$. You simply plug in the masses and the starting velocities, and then use algebra to find the missing final velocity.

The most common mistake is forgetting that momentum is a vector. If two cars are driving toward each other, they are moving in opposite directions. You must make one velocity positive (say, moving right) and the other negative (moving left). If you plug both in as positive numbers, the math will treat them as if they are chasing each other in the same direction, leading to a wrong answer.