The definition of linear momentum follows the formulation of
impulse presented before,
. In this
expression an impulse changes the velocity multiplied by the mass of the object
from where the definition of momentum is extended,
That is, the linear momentum of an object with
respect to a frame of reference is the product of the mass of the object
times the velocity of the object in the frame of reference. From this
definition, the linear momentum of the object depends on the frame of
reference where the velocity is measured. Also, it should be noticed
that the linear momentum of distinct objects moving at the same velocity
can be different because of their masses; for example, a truck and a car
moving at the speed limit in the highway have different linear momentum.
In addition, linear momentum is a vector quantity; thus, the direction
of motion of an object is important when establishing its linear
Also, it should be noticed that because masses are always
positive, the direction of the vector velocity and that of the vector linear
momentum are the same. In the MKS unit system, there is not a special name for the
unit of linear momentum, the units associated to this quantity are the unit of
mass times the unit of velocity
As an illustration of the vector nature of linear
momentum, the two identical trucks (respect to their masses) shown at
the left drawing are moving at the same speed, let us say 60 mph, but
the blue truck is moving due West (or left) while the red truck is
moving toward East (or right). For both trucks the magnitude of theirs
linear momentum are the same. However, following the
convention established before about the sign of vectors, the
direction of motion of the blue truck is specified by assigning to its
linear momentum a negative sign while for the red truck the direction of
motion is specified by indicating that its linear momentum is positive.
Of course, for objects moving in two or three dimension, the vector
nature of their linear momenta is described using the rigorous analysis
Therefore, in general
three dimensional case and
two dimensional case.
Since the impulse is
linear momentum is
following relation between the impulse and the linear momentum can be
Thus, the later relation indicates that an impulse
given to an object results in a change of the linear momentum of the object.
Conversely, if an object changes its linear momentum, it is because an impulse
has acted on the object.
The Impulse on an object is equal to the change in Linear Momentum
of the object.
The following question is a direct application
of the previous formula.