A block is kept on a rough horizontal surface. If we give a variable force F on the block and if we increase the force F continuously then we seem that block remains stationary, which means a same and opposite force is performing on the block by the contact surface. This force is called as frictional force.
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Friction force opposes relative motion or tendency of relative motion. So by showing the Free Body Diagram of block.
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as we increase F , fr will also increase, fr will goes up to a certain value known as fr max and fr max ∝ N where N is a normal reaction force between the contact surface and frmax =μsN where μs is a constant known as coefficient of static friction. If we increase F from fr max then friction suddenly decreases its value up to μkN where μk is the coefficient of kinetic friction and μs ≥ μk .
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Note: Friction is a contact force which replaces the motion when a body tends to move on the surface of another body.
Coefficient of friction ( μ ): It is defined as the ratio of the force of friction (Ff) to the normal reaction (R) i.e μ = Ff/R.
The usually used coefficients of friction are :
(a) Coefficient of limiting friction, μs (Its value is maximum)
(b) Coefficient of kinetic friction, μk (Its value is much smaller than μs ).
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Laws of limiting friction:
1) The magnitude of limiting forces between surfaces is given by Ff ∝ R, where Ff is the frictional force and R is the normal reaction.
F = μR where μ is known coefficient of friction.
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2) The force of friction performs along the interacting surfaces usually in the direction opposite to the direction of motion.
3) The value of coefficient of friction.
(a) Relays upon the nature of interacting surfaces and their irregularities.
(b) Is independent of area of shape or contact of the interacting surface provided the normal reaction remains same.
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Angle of Repose: It is the angle of inclination of a plane at which a body placed on it just begins to goes down. In the figure.
(i) mg is the weight of the body acting vertically downward with components mg sinα normal to the plane downward.
(ii) Normal equation R perpendicular to the plane upward.
(iii) Frictional force Ff opposite to the direction of motion.
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Here 
tanα = μ
Rolling friction: The opposition offered to the circular motion of bodies like sphere, disc, ring, cylinder etc. on another surface is called rolling friction.
The coefficient of rolling friction(μr) is smaller than the coefficient of kinetic friction (μk).
Friction a necessary evil: Friction has various disadvantages but life is impossible without friction because friction has many advantages also.
Inertial frame of reference: The set of rectangular axes obeying the Newton's laws of motion and used to define the position of a particle or an event are called inertial frames of reference. i.e. any set of rectangular axes at in linear uniform motion or rest is an inertial frame of reference e.g. star, earth, pole etc.
Non-inertial frame of reference: The frames of reference which are themselves accelerating, rotating etc. such that Newton's first law of motion becomes invalid in their case can be called as non-inertial frames of reference e.g., an astronaut under a satellite is a non inertial frame of reference with respect to earth.
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