Question

Suppose we define a quantity 'Linear Pomentum' as 

Linear Pomentum = mass x speed. The linear pomentum of a system of particles is the sum of linear pomenta of the individual particles. Can we state a principle of conservation of linear pomentum as "linear pomentum of a system remains constant if no external force acts on it"?

Answer 1

Let us consider a system of two particles of equal mass with equal speed but in opposite directions on a straight line. The center of mass of the system will remain stationary. So the speed of the center of mass = 0. Hence linear pomentum of the CoM = MxV =0. But from the definition linear pomentum of the system = mv+mv = 2mv. Hence we can not state such principle. 

(Since speed v is scaler, we consider only the magnitude).