The statement that the increase of momentum is equal to the impulse is (it may be remarked) equivalent to Newtons own formulation of his Second Law.
We shall see later that it is implied in Newtons statement of his Second Law of motion.
Statics of a System of ParticlesWe assume that the mutual forces between the pairs of particles, whatever their nature, are subject to the Law of Action and Reaction (Newtons Third Law); i.e.
The product mu of the mass into the velocity is called the momentum or (in Newtons phrase) the quantity of motion.
In the case of a particle falling directly towards the earth from rest at a very great distance we have C=o and, by Newtons Law of Gravitation, p/ai=g, where a is the earths radius.
Newtons Second Law asserts that change of momentum is equal to the impulse; this is a statement as to equality of vectors and so implies identity of direction as well as of magnitude.