When the linear momentum of various object is considered,
still a single linear momentum can be assigned to the entire group of objects.
This linear momentum is called the total linear momentum and it is calculated
using the vector addition rules. In fact, the total linear momentum associated
to a group of objects is obtaining solving the vector addition of the linear
momentum associated with the individual objects. Therefore, if
are the
linear momenta of N objects, the total linear momentum of the system is
.

The sequence of drawings presented at the left
correspond to an illustration of how the total linear momentum of a
configuration of objects is calculated. The first drawing of the
sequence shows a set of pool balls moving in all direction just after
the break, .
Since the mass of the pool balls are all the same, the difference in the
length of the vectors representing the linear momentum of the individual
balls is a consequence of their velocities being different. The drawing
of just the vector representing the linear momentum is shown in the
second drawing of the sequence .
The vector addition is a commutative operation; therefore, the addition
of the linear momentum can be done in any order. In this case, the order
selected has for only purpose to maintain the clarity of the drawing
.
The next drawing of the sequence shows the result of the addition of
vectors; that is, the linear momentum of the system. This vector is
obtained following the usual rules for drawing it: ... from the tail of the
first vector placed, in the addition sequence, to the tip of the last
vector added to the addition it is drown the vector representing the
vector addition.
The last drawing of the sequence shows the vector linear momentum of the
system alone
.

Examples

The picture on the left shows an intersection in
downtown Dallas. Only five vehicles are actually in motion while the
remainder are at rest (can you calculate the linear momentum for those
vehicles at rest?). The arrows are the graphical representation of the
linear momentum for those vehicles in motion. The cardinal points are
also represented in the picture. If the masses and velocities are given
in the following table,