# Standard Friction Equation

by Ron Kurtus (revised 21 October 2016)

The standard friction equation shows the relationship between the resistive force of friction, the coefficient of friction and the normal force pushing the objects together. The equation applies in most friction situations.

Questions you may have include:

• What is the standard friction equation?
• What is the coefficient of friction?
• What is the normal force?

This lesson will answer those questions. Useful tool: Units Conversion

## Standard friction equation

The standard equation for determining the resistive force of friction when trying to move two objects or materials with respect to each other shows the relationship between the force of friction, the coefficient friction, and the normal force pushing the two objects together. This equation is written as

Ff = μN

where:

• Ff is the resistive force of friction
• μ is the coefficient of friction for the two surfaces (Greek letter "mu")
• N is the normal or perpendicular force pushing the two objects together
• μN is μ times N

Ff and N are measured in units of force, which are pounds or newtons.

## Coefficient of friction

The coefficient of friction (COF) is a number that determines the amount of friction between materials in contact. It is often designated by the Greek letter mu (μ).

In most cases, the COF is also independent of the area of the surfaces in contact.

Factors determining the COF include combinations of materials, surface conditions, and whether the motion is in the static mode or kinetic mode.

The value of the static COF is greater than kinetic or dynamic COF for the same materials and conditions.

The COF is also different for the various types of friction: sliding, rolling, or fluid. For more information see:

Sliding Coefficient of Friction

Rolling Coefficient of Friction

Fluid Coefficient of Friction

## Normal force

The normal force (N) is the force pushing the two objects or materials together, perpendicular or normal to the surfaces.

In most cases, the COF is independent of the normal force. However, in some cases, N may be so great as to distort the materials, thus changing the COF. Fluids and soft materials are especially susceptible to increasing the normal force.

There are different characteristics for N in sliding, rolling, and fluid friction. For more information see:

Normal Force in Sliding Friction

Normal Force in Rolling Friction

Normal Force in Fluid Friction

## Summary

The standard friction equation is the relationship between the resistive force of friction, the normal force, and the coefficient of friction for the two surfaces.

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## Resources and references

Ron Kurtus' Credentials

### Websites

Friction Resources - Extensive list

Friction Concepts - HyperPhysics

RoyMech (UK) - Friction Factors

### Books

Friction Science and Technology (Mechanical Engineering Series) by Peter J. Blau; Marcel Dekker Pub. (1995)

Control of Machines with Friction (The International Series in Engineering and Computer Science) by Brian Armstrong-Hélouvry; Springer Pub. (1991)

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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friction_equation.htm

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