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
and velocity (v) of the moving body. It is a vector quantity and
is 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)