Coefficient of Friction

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For a detailed understanding of the concept of coefficient of friction, we should be well versed with the idea of friction, friction force, type of friction, etc. Friction can be defined as the resistance to relative motion between two surfaces in contact, i.e., two surfaces might be in contact while sliding, rolling, or in the state of rest. The friction is usually caused due to the rough surfaces. In other words, if the surfaces are not ideal for motion, then relative motion between the two surfaces leads to friction.

The amount of friction will always be directly proportional to the roughness of the surface.

The rougher the surfaces are, the amount of friction will be more. If the surface is smoother, the amount of friction will be relatively less.

Friction Force or Force of Friction:

The friction force is a vector quantity so it has both magnitude and direction. The friction force is a reactionary force. It exists as a reaction of another force that acted upon the body, we can say the friction force can not exist directly. Also, a frictional force is a resistive force.

Coefficient of Friction Formula:

The coefficient of friction is the measure of the amount of interaction between the two surfaces related to friction between two surfaces. The coefficient of friction value will help in determining the roughness of the surface. 

The force of friction depends on or the force of friction is directly proportional to the normal force acting on any object under observation. Mathematically, we can write:

⇒F\[_{r}\] α N …… (1)

Consider a block of mass m placed on a horizontal rough surface (it can even also be an inclined surface). The weight of the object is acting downwards and since the block is in contact with the surface there will be a normal force acting it in the opposite direction of the weight of the object. Let us assume that the block is moving in the right direction then the corresponding friction force will be acting to the left.

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We know that the friction force is directly proportional to the normal force acting on it and the proportionality is replaced by introducing a proportionality constant known as the coefficient of friction. 

Mathematically we write,

⇒F\[_{r}\] = μN ……..(2)


μ - The coefficient of friction

⇒ μ = \[\frac{F_{r}}{N}\] ………(3)

Equation (3) is known as the coefficient of friction formula or the coefficient of friction equation. From equation (3), it is clear that the force of friction is directly proportional to the coefficient of friction. If the coefficient of friction is more, then the corresponding force of friction will also be more.

Static Friction Formula:

Static friction can be defined as the tendency of relative motion when the object is at rest. If the normal force exists between the two surfaces and we slide the object, then the force of static friction acts even before sliding. 

Now, mathematically static friction formula is given by:

⇒ F\[_{s}\] = μ\[_{s}\]N


μ\[_{s}\] - Coefficient of static friction.

⇒μ\[_{s}\] = \[\frac{F_{s}}{N}\]  ……..(1)

Equation (1) is known as the coefficient of static friction formula.

Kinetic Friction Formula:

Kinetic friction is a force that resists the relative motion of the surfaces as they start to move. Then, the kinetic friction formula is given by:

⇒ F\[_{k}\] = μ\[_{k}\]N


μ\[_{k}\] - Coefficient of kinetic friction

⇒ μ\[_{k}\] = \[\frac{F_{k}}{N}\]

The above expression is known as the Coefficient of kinetic friction formula.

Did You Know?

Every material will have a different coefficient of friction depending on the roughness of its surface. For example, if you slide the glass over the glass, you can slide easily without any jerk in the motion. At the same time, if you slide a piece of glass over a road or any unfinished surface, the motion will not be smooth and observe variation in the force. 

Let us have a look at the coefficient of friction of few materials as listed below:


Kinetic friction coefficient 𝞵k

Static friction coefficient 𝞵s

Glass on Glass



Ice on Ice



Aluminum on Steel



Synovial joints of the human



There is also the coefficient of friction calculators available which will ease our calculation while doing numerical.

FAQs (Frequently Asked Questions)

1: What are the Laws of Friction?

Ans: The static friction and kinetic friction are governed by a certain set of rules known as the laws of friction and are given by:

  • The frictional forces are always independent of the measured area.

  • Both limiting static friction and kinetic friction are proportional to the normal force.

2: Does the Coefficient of Friction Depend on the Material?

Ans: Yes. It depends on which material it is in contact with.

3: What is the Skin Friction Coefficient?

Ans: It is a dimensionless parameter explaining the friction force at the boundary between the fluid and wall.

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