What Is Linear Momentum?
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.
Linear Momentum and Newton’s Second Law
In Chapter 3, we introduced Newton’s Second Law as F
However, since acceleration can be expressed as
, we could equally well express Newton’s
Second Law as F
. Substituting p
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