Linear Momentum: It is the product of the mass of a moving object and its velocity. Velocity is constant in linear momentum. Momentum is a vector quantity with the direction same as the velocity.
 |
momentum |
(kg.m/s) or (N.s) |
vector quantity with the direction the same as the velocity |
|
m: |
mass |
(kg) |
scalar quantity |
 |
velocity | (m/s) |
vector quantity |
Impulse:
Impulse is the change in momentum. Impulse is also the integral
of force over time, it is measured in Newton-seconds. Unit of
impulse the same as momentum
(kg.m/s) or (N.s).
Momentum and impulse in two dimensions:
| x
component of the momentum: |
 |
| y
component of the momentum: |
 |
|
x component of the
impulse: |
Δpx = ΣFx. Δt |
| y component of the
impulse: |
Δpy = ΣFy. Δt |
Conservation of Momentum:
If the net force acting on a system of interacting objects is zero, then the linear momentum of the system before the interaction equals the linear momentum of the system after the interaction.
Momentum is conserved both in elastic and inelastic collision.
Conservation of Momentum for colliding objects:
m1.v1 + m2.v2... = m1.v'1 + m2.v'2...
m1: Mass of the
fist object
m2: Mass of the second object
v1: Velocity of the fist object before collision
v2: Velocity of the second object before collision
v'1: Velocity of the first object after
collision
v'2: Velocity of the second object after
collision
Conservation of Momentum in two dimensions for interacting objects have also same rule, and this rule applies for x component of the momentum and y component of the momentum.
m1.v1x + m2.v2x...= m1.v'1x + m2.v'2x... (x component of the momentum)
m1.v1y + m2.v2y... = m1.v'1y + m2.v'2y... (y component of the momentum)
Conservation of Kinetic Energy:
Kinetic energy is conserved in elastic collisions only. Kinetic energy is not conserved in inelastic collisions.
For elastic collision:
0.5 m1.v12 + 0.5 m2.v22 = 0.5 m1.v'12 + 0.5 m2.v'22
Elastic Collision
Momentum is conserved in all kinds of collisions such as elastic, inelastic and completely inelastic collisions in an isolated system.
Kinetic energy is conserved only in elastic collisions. Total kinetic energy after the collision equals total kinetic energy before the collision.
Inelastic Collision
Momentum is conserved in all kinds of collisions such as elastic, inelastic and completely inelastic collisions in an isolated system.
Kinetic energy is not conserved in inelastic collisions. Total kinetic energy after the collision is different from the total kinetic energy before collision. In completely inelastic collision, the objects stick together and the decrease in total kinetic energy will be maximum.
Most of the inelastic collisions, the total kinetic energy after the collision is less than the the total initial kinetic energy before the collisions. However, some inelastic collisions, such as an explosion, the total final kinetic energy of the system is greater than the initial kinetic energy of the system because kinetic energy produced during the explosion.