# The Law of Conservation of Linear Momentum

The law of conservation of linear momentum states that the linear momentum of a system is conserved if there are no external forces acting on that system. This law is universal and one of the most fundamental laws in nature. Nevertheless, experimental verification of the law for a series of cases is not a complicated task. A collision between two objects is an example of a case in which momentum is conserved because the forces that the two objects exert on each other are internal to the system (Loyd 2). The forces exerted on each cart by the other are internal forces. These forces therefore do not change overall momentum of the system. Linear momentum of an object of mass m moving with a velocity v is defined to be: P=mv(1)

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Linear momentum is a vector quantity because it is the product of a scalar (m) with a vector (v). What are the proper SI units of the momentum? Total linear momentum of a system of particles (capital P is frequently used for this quantity) is defined as vector sum of individual momenta:P=P+P+P…=∑P. It can be shown that the total linear momentum of the system is constant if there are no external forces acting on the system. This statement is referred to as the law of conservation of linear momentum. The following formulation of the law is convenient for applications: if there are no external forces acting on the system, its total momentum before an event (e.g. collision between the objects that belong to the system) is equal to the total momentum of the system after the event. Since linear momentum is a vector quantity, this statement means that both the magnitude and the direction of the total momentum are preserved during the collision (Loyd 6). The forces exerted between the particles of the system are called “internal forces,” and they cannot change the total momentum of the system. Please note that momenta of individual particles in the system may change with time as a result of internal interactions with other particles of the system. However overall momentum of an isolated (no external interactions) system is conserved.

If P andP stand for the initial momenta of the participants of the collision (objects 1 and 2) and P and P stand for their final momenta after the collision then P+P=P+P (2)

## Reference

Loyd, David. Physics laboratory manual. New York: Brooks Cole, 2002.

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