Conservation of Momentum: What Is It, and Why Should You Care?

football collision conservation of momentum example

Credit: Public Domain

By Andrew Bennett

Conservation of Momentum Definition

The conservation of momentum is enormously useful, particularly for learning about collisions between objects. Mostly used to describe the collisions of two or more objects, this physics principle means that the total momentum does not change in a closed system. In other words, the total value of momentum is constant when there are no external forces acting on a group of objects.

Conservation of Momentum Equation

Typically, we use an equation that comes from a special case of the Impulse-Momentum Theorem:

When the force on the system is zero, the total momentum does not change. So, we can write an equation stating that the initial total momentum is equal to the final total momentum.

This equation can be expanded by including momentum terms for each object. For example, if we have two objects labeled A and B, respectively, we might write this as:

We could also substitute the equation for momentum into each term and get the result:

Using a known value for total momentum, we can then solve for the velocity of an object before or after a collision.

Video: Momentum Conservation Explained

In this video, you will learn more about the momentum conservation equation. Then, you will learn to solve an example problem involving a person jumping off a skateboard.

Additional Momentum Practice Problems

Since momentum is a vector quantity, we could apply this in two or even three dimensions by treating each dimension separately. To learn how to solve problems like that, be sure to check the rest of the momentum playlist. For an example that combines momentum and energy conservation, check out this video. While you're on YouTube, make sure to subscribe to my channel, as well.

Questions?

If you have questions about the information in this post or the accompanying video, please let me know! I'm happy to help.

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