This post is entirely focused on the **Friction coefficient** (also known as the **coefficient of friction**). We will define it and find out its types. Also we will derive equations and get a list of values. Please note the symbol **μ**(mu) which denotes this coefficient.

## What is the friction coefficient?

The **Friction coefficient** is a constant for a pair of surfaces (made of same or different materials) in contact which decides the amount of frictional force generated at the common layer when one surface moves or tends to move with respect to the other surface.

This coefficient **μ** is presented generally in this way: **μ** = **F /N** = ratio of frictional force and Normal reaction force.

It has 2 different sets of values for a pair of surfaces and these are known as

1] the **Coefficient of static friction** **μ**_{s} and

2] the **Coefficient of Kinetic friction** **μ**_{k}

## What is the equation or formula of the **Friction coefficient**?

The equation is like this: **μ** = **F /N** = ratio of frictional force and Normal reaction force.

### What is the Coefficient of static friction?

The** coefficient of static friction** is the ratio of the **Limiting friction **(maximum possible static friction) and the Normal reaction force.

### What is Limiting Friction?

For **static friction** (when there is a tendency of movement of a layer with respect to another surface layer but there no actual movement yet), the maximum possible frictional force before the object starts moving is called the Limiting Friction.

### Derive the equation of the Coefficient of static friction

The maximum static friction force or the **Limiting friction** F_{smax} is directly proportional to the normal force or normal reaction force N.

F_{smax} ∝ N or F_{smax} = μ_{s} N.

Hence, μ_{s} = F_{smax} / N

This μ_{s} is a constant for 2 surfaces in contact and for static friction. This is called th**e coefficient of static friction** between the 2 surfaces involved.

### What is the formula for static friction?

As the limiting friction is the max possible static friction, so we can write the expression of static friction as F_{s} <= F_{smax}

or, **F**_{s}** <= μ**_{s}** N **

### What is the Coefficient of kinetic friction?

The coefficient** of kinetic friction** is the ratio of the kinetic frictional force and the Normal reaction force.

### Derive the equation for Coefficient of kinetic friction

For **Kinetic friction** F_{k} (when there is actual relative motion between 2 surfaces in contact), the frictional force is again directly proportional to the Normal reaction force N.**F**_{k}** ** ∝ **N or F**_{k}** = μ**_{k}** N **

Hence, **μ**_{k}** **= **F**_{k} / **N**** **

This μk is a constant for 2 surfaces in contact and for kinetic friction. This is called the coefficient of kinetic** friction** between the 2 surfaces involved.

## What is the Friction Coefficient table?

This table consists of the **μ**_{s} and the **μ**_{k} for different material pairs.

The values of these coefficients totally depend on what surfaces (material wise) are in contact where relative motion is happening or tending to happen.

We provide a set of such constants for different material pairs in a **friction coefficient table**. This table is also known as th**e Coefficient of Friction** **chart**.

### The Friction Coefficient table – Sample Values for different materials

As an example, if we take the value of μs and μk for 2 wood surfaces in contact, we can easily observe that μk is less than μs.

This is true for all other material pairs in the above list. This clearly explains why the kinetic friction magnitude is less than static friction(generally).

Also find 2 interesting readings above: (1)Steel on dry steel and (2)Steel on oiled steel. It shows how lubrication reduces the value of friction.

### What is the unit of **μ?**

Being a ratio of 2 forces, it has no unit. It is just a number.

### What is the frictional coefficient of steel on steel?

For steel on steel, dry the values of μs and μk are respectively 0.6 and 0.3.

For steel on steel oiled the values of μs and μk are respectively 0.05 and 0.03

### What is the **μ** of Teflon on steel?

It is 0.04 (both **μ**_{s} and **μ**_{k} )

### Static friction and Kinetic friction – can we discuss briefly?

When an object is static then due to molecular-level cohesion between its surface and the other surface on which it is resting, we need to apply a force to move it. As we increase the magnitude of the force the opposing force (friction) also increases linearly up to a maximum value called limiting friction. Now if apply our force beyond that Limiting friction, the intralayer cohesion is won over and the two surfaces now start experiencing relative motion.

At that point, the friction drops quickly from the maximum level of static friction(as mentioned earlier as limiting friction) to a little lower level and remain constant (kinetic friction) till the object is pushed to move and other criteria like normal reaction force and the sliding material remains unchanged.

Coming back to molecular cohesion theory, as you are pushing and it’s moving or sliding (facing the kinetic friction) the object’s surface is not getting enough time to get his cohesion with the sliding layer back. So during this sliding time, you are pushing with less amount of force just to maintain the speed winning over the kinetic friction.

## **μ** – What next?

We will publish a list of numerical on **Friction coefficient** here very soon. Pls, visit the site and this page soon.

Definition of Friction