Linear momentum is a vector quantity defined as the product of an object’s mass, m, and its velocity, v. Linear momentum is denoted by the letter p and is called “momentum” for short:

Note that a body’s momentum is always in the same direction as its velocity vector. The units of momentum are kg · m/s.

Fortunately, the way that we use the word momentum in everyday life is consistent with the definition of momentum in physics. For example, we say that a BMW driving 20 miles per hour has less momentum than the same car speeding on the highway at 80 miles per hour. Additionally, we know that if a large truck and a BMW travel at the same speed on a highway, the truck has a greater momentum than the BMW, because the truck has greater mass. Our everyday usage reflects the definition given above, that momentum is proportional to mass and velocity.

In Chapter 3, we introduced Newton’s Second Law as F = ma. However, since acceleration can be expressed as , we could equally well express Newton’s Second Law as F = . Substituting p for mv, we find an expression of Newton’s Second Law in terms of momentum:

In fact, this is the form in which Newton first expressed his Second Law. It is more flexible than F = ma because it can be used to analyze systems where not just the velocity, but also the mass of a body changes, as in the case of a rocket burning fuel.