Where:

Note that there is no restriction in the way the particles are connected. As a result, the above equation will also hold true for a rigid body, a deforming body, a liquid, or a gas system.

Now, we can rewrite the above equation as

where

The above equation can be expressed as

Integrating both sides from time

which becomes

The term

is defined as the external linear impulse acting on the system of particles (between

We define the linear momentum for the system of particles as

Therefore, equation (1) can be written as

Note that there is no restriction in the way the system of particles are connected. As a result, the above equation will also hold true for a rigid body, a deforming body, a liquid, or a gas system. To see an example problem involving impulse and linear momentum see Rocket Physics.

If no external forces act on the system of particles, then

Linear momentum is therefore conserved for the system of particles (between

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