The Law of Conservation of Momentum

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  • 0:04 What Is Momentum?
  • 0:50 Conservation of…
  • 1:16 Law of Conservation of…
  • 2:23 Momentum of a Brick Wall
  • 3:27 Example Problem
  • 5:16 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After completing this lesson, you will be able to explain what conservation of momentum is and use the equation for conservation of momentum to solve problems. A short quiz will follow.

What Is Momentum?

If I said to you, 'That guy has some serious momentum,' what would it mean to you? In general conversation, it means he's moving forward in whatever he's doing and he'll be hard to stop. But momentum is also a concept in physics. What does momentum mean there?

Well, momentum has clearly got something to do with movement. And larger objects are harder to stop too, so it seems like big things have a lot of momentum as well. And that's pretty much exactly what it is. Momentum is about velocity and mass. A large football player running fast across the field has a lot of momentum. He has a large mass and a large velocity. A huge truck barreling down the highway at 70 miles per hour has a lot of momentum for the same reason.

Conservation of Momentum Equation

So we know kind of what momentum is. But how do we put a number to it?

The equation for momentum looks like this:

p = mv

This is where p is the momentum of an object, measured in kilogram meters per second; m is the mass of that object, measured in kilograms; and v is the velocity of the object, measured in meters per second (or meters divided by seconds).

Law of Conservation of Momentum

The law of conservation of momentum says that momentum only moves from one place to another, since it's neither created nor destroyed.

So let's say that the truck barreling down the highway crashes into a small car, causing it to slow down. It just lost momentum. But momentum can't be destroyed, so where does the momentum go? It goes into the small car, which will now be moving at a different speed (probably faster) than it was before. The momentum transferred from the truck to the smaller car. Momentum was conserved.

But we do have to be careful. Momentum is a vector, which means it has both size and direction. The direction the object is moving matters. Only the total momentum of the whole system has to be conserved. If you have one car moving right with 4 kilogram meters per second of momentum and one car moving left with 4 kilogram meters per second, the total momentum of the system is zero; the two cancel out. So if the two cars crash together and stop, momentum has been conserved just fine because there wasn't any overall momentum at the start.

Momentum of a Brick Wall

But what happens if the truck crashes into a brick wall and stops? Surely momentum has been destroyed then, right? It's hard to imagine how momentum could still be conserved, but it is. In this case, momentum is transferred into a mixture of the molecules in the wall moving faster and the earth itself spinning more in that direction. The earth and the molecules in the wall took the momentum.

The equation for conservation of momentum looks like this:

  • total momentum before = total momentum after
  • pbefore = pafter
  • (m1v1 + m2v2)before = (m1v1 + m2v2)after

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