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Friction
Place a ball on a table and give it a push. The ball moves some distance and comes to rest. According to Newton's First Law, a body in motion should be in motion until and unless some external force acts on it. But in the above example, we see that though no external force is acting on the body, the ball comes to rest.
According to Newton's Second Law, a retarding force must be acting on it as it moves.
This force

a) opposes motion,
b) is always tangential to the surface in contact and
c) acts in a direction opposite to the direction of motion of body.

This force is called the force of friction. Thus, we define friction as an opposing force that comes into play when one body actually moves or tries to move over the surface of another body.
Consider a block sliding over a horizontal surface. If the block slides in the direction AB

Frictional Force is always in opposite direction to the applied force

the force of friction acts in opposite direction. If the direction of motion is reversed and the block moves in the direction AC, the force of friction ?f? is reversed and acts opposite to AC.

Origin of sliding friction
Friction is a surface phenomenon. The surface of a body has some irregularities however smooth it may be. The roughness of the surface is the cause of friction. When a force is applied on one body to make it slide over the surface irregularities, an opposing force is developed. This is the force of friction. If applied force is increased, the resistive force also increases. But at a particular limit, the applied force overcomes the friction force and the body starts to slide over the surface of another.

Limiting friction
Consider a block of weight mg placed on a flat surface and one end of a string attached to the block and other end of it carries a weight pan as shown in the figure.

Frictional Force is always in opposite direction to the applied force

Place a small mass in the pan, a horizontal force F acts on the block. We see that the pan does not move. The friction force 'f' completely balances the force F applied. If we add more mass to the pan the block still does not move. The force of friction increases to balance the increased applied force. If the mass added in the pan is gradually increased, a stage is reached when the block just begins to slide over the horizontal surface. At this stage, the force of friction is given by the total weight where m is the mass of the pan and the mass added to it. The maximum or limiting value of the force of friction, which comes into play when a body just begins to slide over the surface of another body, is known as limiting force.
The block exerts its weight (w = mg) on the horizontal surface on which it is resting in the downward direction. The horizontal surface exerts an equal and opposite reaction, force R, vertically upwards normal to the surface, which is called as normal reaction. These forces are in equilibrium. The only horizontal force acting on the block is the applied force F.

The Law of Limiting Friction
From various experiments it is seen that three empirical laws are found to be obeyed by a limiting friction.

The magnitude of the force of limiting friction depends upon the nature of the surface in contact and on their roughness. It is independent of the area of the surface in contact.
The force of friction is tangential to the surface in contact and its direction is opposite to the direction of motion of the body.
The value of limiting friction between two given surfaces is proportional to the normal reaction between them.
where is a constant of proportionality and is known as the coefficient of limiting friction.

where

is a constant of proportionality and is known as the coefficient of limiting friction.

Experimental Verification
Take a smooth regular block of wood and place it on a horizontal smooth surface. Let its mass be m. The normal reaction R is given by R = mg where g is acceleration due to gravity. Gradually add weights in the pan until the block just begins to slide on the surface. Weigh the pan along with its contents. Let the total mass be 'm'. Therefore, applied force F = mg. The value of F is the limiting static friction f_s. The coefficient of limiting static friction is given by

For smooth wooden block U_s is found to be approximately 0.2. Now, place an identical block on the first block. The normal reaction is doubled. It will be seen that twice the force is required to just make them slide over the same surface. This shows that limiting friction is proportional to the normal reaction. The ratio for coefficient of friction

remains unchanged. Now, connect the two blocks together and place them one behind the other. The surface area in contact with the horizontal surface is doubled, but the value of limiting friction remains unchanged showing that it is independent of the areas of the surfaces in contact.
Now, use two identical blocks but of different material. You will find the difference in limiting friction. This shows that limiting friction depends on the nature of the surface in contact. The value of friction changes with the condition of surface, grain, contamination, moisture, etc

Approximate values of the coefficient of limiting friction for some surfaces

Spheres in contact	Coefficient of friction
Spheres in contact	Limiting	Kinetic
Steel on steel	0.25	0.18
Steel on glass	0.30	0.20
Steel on wood	0.40	0.22
Wood on glass	0.46	0.24
Wood on wood	0.50	0.26
Leather on wood	0.55	0.40
Car tyre on metalled road (for small speed)	0.60	0.40
Steel on steel (greased)	0.10	0.05

Kinetic or Sliding Friction
The force required to just make a body slide over the surface of another is limiting frictional force (f_s). But the force necessary to maintain a body in uniform motion over the surface of another body after the motion has started measures the kinetic or sliding friction (f_k) between the two surfaces.

The ratio

is called coefficient of kinetic friction.

is always less than

Rolling Friction
When a body rolls on a level track the area of contact is very small. So, pressure exerted is very large. This causes depression below and mount on the front as shown in the figure below.

Rolling friction caused due to depression

While rolling, the body has to come up the depression and climb the mount. This type of friction is rolling friction, but when the surface is hard there is no depression or mount. The actual area of contact is small. The adhesive pressure becomes large and rolling friction increases. But for some magnitude of normal reaction, the rolling friction is less than the sliding friction

This is the reason why all vehicles are provided with wheels.

Angle of friction
The angle of friction is defined as the angle that the resultant of the limiting friction and normal reaction makes with the normal reaction.

Angle of friction

As shown in the figure, the resultant of limiting friction (F) and normal reaction (R) makes an angle

with normal reaction. By definition,

is angle of friction.

But

, coefficient of limiting friction

... (i)

Hence, coefficient of friction is equal to tangent of the angle of friction.

Angle of Repose
The angle of repose is defined as the angle of the inclined plane at which a body placed on it just begins to slide.
Let?s consider an inclined plane, whose inclination with horizontal is gradually increased till the body placed on its surface just begins to slide down. If

is the inclination at which the body just begins to slide down, then

is called the angle of repose.
The following forces are acting on the body:

The weight Mg of the body acting vertically downwards.
The limiting friction F in upward direction along the inclined plane which in magnitude is equal to the component of the weight Mg acting along the inclined plane, i.e.,

F = Mg sin ... (ii)

The normal reaction R acting at right angle to the inclined plane in upward direction is equal to the component of weight acting perpendicular to the inclined plane, i.e.,

R = Mg cos

... (iii)

Dividing equation (ii) by equation (iii), we have

Since

... (iv)

Angle of repose

Therefore, coefficient of limiting friction is equal to the tangent of the angle of repose.
From equations (i) and (iv), we have

i.e., angle of repose is equal to angle of friction.
Points to remember:

1) Friction is an opposing force that comes into play when one body actually moves or tries to move over the surface of another body.
2) Coefficient of friction is equal to tangent of the angle of friction.
3) Kinetic friction is always less than static friction.
4) Angle of repose is equal to angle of friction

Hope it helps you in anyway.

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