# Rolling Friction or Rolling Resistance

by Ron Kurtus (revised 15 January 2016)

Rolling friction is the resistive force that slows down the motion of a rolling ball or wheel. It is also called rolling resistance.

When a force or torque is applied to a stationary wheel, there is a small static rolling friction force holding back the rolling motion. However, resistance from static sliding friction is what really causes the wheel to start rolling.

Once it is rolling, the resistance to the motion is typically a combination of several friction forces at the point of contact between the wheel and the ground or other surface.

A simple version of the rolling friction equation is similar to the Standard Friction Equation.

Questions you may have include:

• What is the resistance to starting rolling?
• What factors play in kinetic rolling resistance?
• What is the rolling friction equation?

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

## Resistance to starting rolling

When a force or torque is applied to a stationary wheel, there is a small static rolling friction that resists the rolling motin. However, it is too small to make much of a difference. Instead, static sliding friction prevents the wheel from simply sliding along the surface, resulting in the wheel rolling forward.

Static sliding starts wheel rolling

(See Starting Rolling Motion for information.)

## Kinetic rolling resistance

Once a wheel is rolling, several factors inhibit its motion.

### Elastic deformations

Since even hard materials can deform slightly when pressure is applied. Those deformations on the surfaces in contact are major factors in inhibiting the rolling motion.

Slight deformation of ground and rolling wheel

### Surface irregularities

The surface of the wheel and what it is rolling on are not perfectly smooth. They have irregularities.

Close-up showing surface roughness

This surface roughness is a reason for the resistance to rolling motion. It causes a "jiggle" when the wheel is rolling.

### Molecular friction

Molecular friction is caused by the molecular attraction or adhesion of the materials. It is like a "stickiness" factor. When materials are pushed together, molecular forces try to prevent them from being pulled apart. This can be seen in highly polished metals and certain materials such as rubber.

As an extreme example, you could put double-sided tape on the rim of a wheel and see the resistance to rolling from the sticky tape.

## Rolling friction equation

The general equation for rolling friction is:

Fr = μrN

where:

• Fr is the resistive force of rolling friction
• μr is the coefficient of rolling friction for the two surfaces (Greek letter "mu" sub r)
• N is the normal force pushing the wheel to the surface

This equation is a simple version of the resistance to rolling motion. More complex versions include the effects of wheel diameter and speed.

### Normal force

If the object is rolling on a level surface, the normal force N is the weight of the wheel and any vehicle pushing on the wheel axle.

### Coefficient of rolling friction

Examples of the coefficient of rolling friction include:

• Train wheel on steel track: 0.001
• Ordinary car tire on dry pavement: 0.015
• Truck tire on dry pavement: 0.006-0.01

## Summary

Rolling friction (or rolling resistance) is the resistive force that slows down the motion of a rolling ball or wheel.

When a force or torque is applied to a stationary wheel, static rolling friction holds back the motion. Once the wheel is rolling, the resistance to the motion is typically a combination of several friction forces at the point of contact between the wheel and the ground or other surface.

A simple version of the rolling friction equation is similar to the Standard Friction Equation.

Roll with the punches

## Resources and references

Ron Kurtus' Credentials

### Websites

Friction Resources - Extensive list

Rolling friction and rolling resistance - includes coefficients - Engineering Toolbox

Rolling Friction - simple explanation - Davidson College

Rolling Resistance - Wikipedia

### Books

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.

## Students and researchers

www.school-for-champions.com/science/
friction_rolling.htm

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