Friction: Friction is the retarding force which acts tangentially to the contact surface when a body actually moves or tends to move over the surface of another body.
Static friction: The force of friction which exactly counter-balance the applied force during the stationary state of a body is called static friction. So static friction is equal to the applied force. Static friction increases up to the maximum value (limiting friction) with increasing the applied force. So static friction is self-adjusted force.
Limiting friction: The maximum value of static friction which comes into play when a body is just going to start sliding over the surface of another body is called limiting friction.
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Laws of friction:
1. The direction of limiting friction is always opposite to the direction in which motion takes place or tends to take place. The force of friction acts tangentially along the surface of contact of two bodies.
2. The magnitude of frictional force (f) is directly proportional to the normal reaction (R) between the surfaces. 
then 
where 
is the coefficient of friction.
3. Friction is independent of area of surface of contact of two bodies and depends on the nature of the surface.
Angle of friction: The angle between the normal reaction and the resultant of limiting friction and normal reaction is called angle of friction.
The resultant of limiting friction (f) and normal reaction (R) is represented by 
= OC.
The angle 
between R and is called angle of friction. So, tan = 
 but = . So, tan = .
The coefficient of friction is numerically equal to the tangent of the angle of friction.
Angle of repose: The minimum angle made by the inclined plane with the horizontal surface such that the body lying on the inclined plane is just at the verge of sliding down along the inclined plane is called angle of repose.
A body of mass m is placed on the inclined plane of inclination 
then the component of weight acting downward is F = mgsin and normal reaction force R = mgcos . As the body remain at rest then, frictional force f = F = mgsin again where is the coefficient of friction.
So, = Â = 
= tan ——-(1)
If is the angle of friction, then, tan = —-(2)
From equations (1) and (2) we get, tan = tan so, = .
Therefore, angle of friction = angle of repose.
Acceleration of a body on rough horizontal plane: A body of mass m is moving on rough horizontal plane due to force F. If fk is the frictional force then, fk = µkR where R (= mg) is the normal reaction force. Then the acceleration of a body a = (
– µkg).
Acceleration of a body on rough inclined plane: A body of mass m is placed on the inclined plane of inclination ( > the angle of repose). The force acting downward along the inclined plane is F/ = mgsin —-(1).
The frictional force fk acts upward along the inclined plane. fk = F = µkR where µk is the coefficient of kinetic friction.
The normal reaction force R = mgcos ——(2).
As the body moves downward along the inclined plane, then, ma = F/ – F = mgsin – µkmgcos .
Or, a = g( sin – µkcos)
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