What is momentum? And what would cause a train to crash through the wall of a train station onto the street below? Hint: They both can be answered pretty much the same way!

Sir Isaac Newton described momentum (p) as a quantity of motion. He originally stated his second law in terms of this quantity of momentum. The rate of change of the momentum of an object is equal to the force applied to the object. Mathematically, we say:

So what does all of this mean?

Let’s start with basic definitions of terms. We have already discussed mass (m) and velocity (v). Mass is a scalar quantity (magnitude only, direction has not meaning. An object cannot have “negative” mass). Velocity, on the other hand, is a vector quantity. Not only does it have magnitude (how fast the object is moving) but it also must
have a direction (north-south, up-down, left-right, etc. It is generally convenient for us to call one direction, such as “up” or “to the right” as positive, and the other direction, such as “down or “to the left” as negative.

Momentum will have the symbol “p” and it is expressed as the product of the mass times the velocity. In other words,

momentum = mass x velocity



The units of momentum will be

And this will sometimes be expressed as

One way to explore momentum and impulse is to think about cars. Think of momentum as a truck and a Volkswagen.....

You would think that a truck  would have more momentum than a little Volkswagen, but actually they can have  the same momentum; it just depends on the speed the vehicles are traveling at.

If the truck weighs 3000 Kg and is traveling at 5 m/s, it’s momentum is (3000 kg)(5m/s) = 15,000 kg m/s.

On the other hand, if the volkswagon has a mass of 500 kg but is travelling at 30 m/s, it also has a momentum of 15,000 kg m/s.  Both have the same momentum.  If they are travelling in opposite directions, then their magnitudes are equal but we can say that one of them has a momentum of -15,000 kg m/s.

When we talk about the total momentum of a system, we are talking about the sum of the momentums (momenta) of each individual particle or piece of the system. 

Often, it is useful to see what someone else has to say on the topic; Check out these lessons from "The Physics Classroom" (Glenbrook High School). Each contains some practice problems at the end of the lesson.


Momentum and Impulse Connection

Real World Applications

Giancoli Multiple Choice Practice Questions (Select "Practice Problems) and try some - Don't worry if you can't do all of them yet.