Conservation of momentum
When a bullet is shot from a gun, the gun recoils, so that sum of bullet's momentum and the gun's momentum in the opposite direction, cancel out and the final momentum and initial momentum of the system is equalized.
If a ping pong ball and a football are rolling towards you at the same speed, you will notice that to bring them to a halt, you will have to apply larger force on the football. The ping pong ball stops easily. In another situation, if two footballs are moving towards you at different speeds, then you will notice that the football with the higher speed is more difficult to stop. It appears from these observations that the force applied (and time duration for which the force is applied) to bring about any change in motion, depends on both the mass and the velocity of the body. There is inertia of motion. A term momentum is used to describe this inertia or quantity of motion.
Momentum is denoted by p. Momentum is the product of mass (m) and velocity (v) of the moving body. It is a vector quantity andis written as
Since m is a scalar and v is a vector quantity, momentum is a vector quantity. It has same direction as the velocity of a body.
The standard unit for measuring momentum is kg.m/s or kilogram–meter per second. We can see from the definition that a moving object can have a large momentum if either its mass or its velocity is large.
Relation between K.E and linear momentum
We know, K.E = 1/2 mv2 ------> (ii)
From (i) and (ii) we have
K.E = p2/2m ------> (iii)