# Starting Rolling Motion

by Ron Kurtus (revised 20 November 2016)

A wheel or ball on a surface is held there by static sliding friction. In order to start the rolling motion, a force or torque must be applied to the wheel. The force of the static sliding friction prevents the wheel from sliding and thus initiates the rolling motion. The rolling motion is actually a form tilting about the point in contact.

Questions you may have include:

• How is rolling like pivoting about a point?
• How does friction cause rolling when torque is applied?
• How does friction rolling when a push is applied?
• How do treads on a soft surface help?

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

## Rolling and pivot points

You can look at how rolling is started as if the wheel is pivoting about its point of contact on the ground, where it is held in place by static sliding friction. The pivoting results the next part of the wheel surface touching the ground to become the new pivot point.

Wheel rolls from one pivot point to another

## Applying torque to the wheel

Applying a torque on the axle of a wheel will cause the wheel to roll, provided there is static sliding friction resistance at the point of contact with the other surface. If there is negligible static sliding friction at the point of contact—such as a wheel on ice—the wheel will simple spin.

### Force on edge from torque

A torque is a rotational force applied to the axle of a wheel, causing it to rotate. The relationship between torque and the force at some distance from the axle is:

τ = rFe

or

Fe = τ/r

where

• τ (Greek letter tau) is the torque in foot-pounds or newton-meters
• r is the radius or distance from the center in feet or meters
• Fe is the force in pounds or newtons at the edge of the wheel

Torque creates a force at edge of wheel

### Friction causes forward motion

The force, F, is resisted by the static friction at the point of contact of the wheel and the ground or other surface. This resistance causes the wheel to roll forward.

The force moving the wheel forward is the torque force at the edge minus the static friction:

F = Fe − Ff

where

• F is the force moving wheel forward
• Fe is the force at the edge of the wheel
• Ff is the static sliding resistive force of friction

Torque resisted by friction results in rolling forward

### Starts spinning

If the force from the torque is much greater than the static friction (Fe >> Fr), the static friction will become kinetic or sliding friction and the wheel will start spinning, since the kinetic coefficient of friction is less that the static coefficient of friction.

Although the wheel will roll forward, since it is also spinning, the forward speed will be less than if it was not spinning.

## Pushing or pulling the wheel

You can also cause a wheel or ball to roll by pushing on it. Again, the wheel is prevented from sliding forward by the static friction at the point of contact. In this case, the static friction is preventing the wheel from sliding forward and is in the opposite direction.

Pushing on a wheel starts it rolling

If the wheel is on an incline, the force of gravity will pull on the wheel, the same principles apply and the static friction will causing the wheel to roll as it is pulled down down the slope.

If the wheel or tire has treads and is being turned by a torque on its axle, a new factor comes into play when the other surface is soft. In such a situation, the treads will dig into a soft surface and dramatically increase the traction. Typically, a soft surface material—such as mud or snow—has a much lower coefficient with a tire or wheel. Thus, the treads are necessary to create sufficient traction to move the wheel (and its vehicle) forward.

Treads dig in and help the wheel roll forward

Snow tires and tires made for driving in mud have treads that will dig into the soft surface and allow the tire to roll forward. Most everyday automobile tires have a majority of their treads aligned to prevent water from creating a lubricating layer that would cause sliding during a rainstorm.

## Summary

A wheel will start rolling when a force is applied and there is a resistive force or friction at the point of contact with the ground. The force may be a torque or a linear push on the wheel. Static friction causes the rolling motion. It is also called the traction of the wheel.

Stay in good condition

## 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 - mathematical approach - MathWorks

Rolling Resistance Equations - derivations - Real World Physics Problems

### Books

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## Students and researchers

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

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