MOMENTUM

Definition 

Momentum of a body is the product of its mass and velocity. 
                                                                                                   OR 
The quantity of motion of a body is called its momentum. 

Mathematically 

If "m" is the mass and "v" is the velocity of a body then Momentum P is given by: 
                                                                         P = mv 

Unit 

In M.K.S. system the unit of Momentum is kg-m/s or N-s 

Nature 

It is a vector quantity. Its direction is same as that of velocity, 

LAW OF CONSERVATION OF MOMENTUM 

Statement 

The total momentum of a system remains constant provided no external forces act on it. 
                                                                         OR 
The Momentum of an isolated system always remains constant. 

PROOF 

Consider a system consisting of two balls A and B of masses m₁ and m2 moving in a straight line, with velocities U1 and U₂. On colliding with each other they move with velocities V1 and V₂ respectively as shown in the figure. 
The total Momentum of the system before collision= m₁U1 + m₂U₂ 
The total Momentum of the system after collision = m_1V1 + m_2V2 
According to the law of conservation of Momentum Initial momentum = Final momentum 
                                                              m₁U1 + m₂U₂ = m1V1+ m₂V₂ 

Hence the Momentum of a system remains constant. 

FRICTION  

Definition 

When two bodies are in contact with each other and the force is applied to the upper body to make it move over the lower body, an opposing force is developed in the plane of contact which resists the motion. This force is called friction. 

                                                                          OR 

When one bod / slides over the surface of another body, an opposing force is set up to resist the motion. The force which opposes the motion is called friction. 

CAUSES OF FRICTION 

There is no ideal smooth surface present in universe. Each surface has elevations and depressions which causes to friction. 

When two surfaces are brought into physical contact. the elevations of one impacts into the depressions of first or vice versa which causes an inter locking with two surfaces. This interlocking opposes the relative motion of one surface on the other.