# Linear Momentum: Definition, Equation, and Examples

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• 0:01 What Is Momentum?
• 2:06 Examples of Momentum
• 3:52 Lesson Summary

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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Any moving object has momentum, but how much momentum it has depends on its mass and velocity. In this lesson, you'll identify linear momentum, as well as see examples of how an object's momentum is affected by mass and velocity.

## What Is Momentum?

If you're standing at the bottom of a hill and you're faced with the option of stopping a runaway semi-truck or stopping a runaway bicycle, you'd probably choose to stop the bike, right? The reasoning behind this is that the semi-truck has more momentum than the bike. Momentum simply means mass in motion.

The semi-truck has a large momentum because it is very massive, but it also has a large speed, which influences momentum, as well. The bike also has momentum because it has a large speed, but because its mass is less than that of the truck, its momentum is also less.

This relationship can be described in an equation: momentum = mass x velocity. You may remember that velocity is speed with direction, so if an object has a large speed, it also has a large velocity. Our momentum equation can be simplified even more by substituting the words for symbols: p = mv, where p is momentum, m is mass (in kg) and v is velocity (in m/s).

As you can see, if you increase one of the variables on the right side of the equation, either the mass or the velocity, the momentum on the left side must also go up in order to keep both sides equal. If you increase both mass and velocity, the momentum goes up even more. In this way, we can see that both the bike and the semi can have a large momentum, but the semi's is still more because it is far more massive than the bike.

This also means that an object at rest does not have momentum. The velocity of an object at rest is zero, so there's no movement. In order for an object to have momentum, it must be moving!

An important thing to note about momentum is that it is a vector quantity. This means that it has both magnitude and direction. Velocity is also a vector quantity because it has both of these components, and fortunately for us, the direction of the momentum is the same as the direction of the velocity vector. But in order to fully describe the momentum of an object, you must include its direction - otherwise, it's not a vector.

## Examples of Momentum

As you now know, an object of any size can have a large momentum because it depends on the speed of the object as well as its mass. A supertanker ship that is coming into port may not be traveling very fast through the water, but it is quite massive, so it needs to begin slowing down long before it gets to port in order to be able to dock safely.

Let's say that our bike speeding down the hill is one-half of the semi-truck's mass but is traveling twice as fast. In this situation, each vehicle has the same momentum. That may sound a bit far-fetched, so let's look at it in the equation. For the truck, the momentum is p = 2m * v. The bike's momentum is p = m * 2v. Can you see how this would equal the same momentum for both vehicles?

As long as you know the mass and velocity of the object, you can determine its momentum. A 5 kg ball rolling at 10 m/s to the right has a momentum of 5 kg * 10 m/s, or 50 kg * m/s to the right.

If that same ball increases its speed to 20 m/s, we simply double the momentum since the velocity component is doubled. The new momentum for this ball is 100 kg * m/s.

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