The momentum of a single particle is a vector defined as the product of its mass and its velocity . That is
Suppose that instead of a single particle we have a system of n particle with masses m1, m2 … etc, and their velocities v1 and v2 etc. respectively then the total momentum in a particular reference frame is,
The vector sum of all external forces is given as,
Taking its components along x-direction and y-direction we can write
This is nothing but Newton's second laws of motion. Note that no internal force will be used in this expression and only external forces will be used.
Conservation of Linear Momentum
If the sum of the external force acting on a system is zero. Then,
or = constant.
So, when the resultant external force acting on the system is zero, the total vector momentum of the system remains constant. This is called the principle of the conservation of linear momentum. The momentum of the individual particles may change, but their sum remains constant if there is no net external force.
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