Rolling Friction

Rolling Friction - Coefficient, Formula and Examples of Rolling Friction

Sir Isaac Newton once wondered why apples on the trees fall to the ground. Trying to find an answer to this question, he proposed the laws of gravity in 1687 and gave an answer to his own question. But if gravity acts downwards, why do things which are pushed forwards on a surface eventually stop? Why do the wheels of a cart that is pushed forward eventually stop? Why do we need to maintain a pushing force when we want to push something to a spot some distance away? Attempts to answer such questions were made by Leonardo da Vinci as early as 1493 when he documented the classic laws of sliding friction in his unpublished notebook. These laws were rediscovered in 1699 by Guillaume Amontons. Friction is the force which resists motion between two surfaces which are sliding against each other. There are various kinds of friction. And one among them, which concerns bodies that are in motion by rolling across a surface.

If you kick a football, it will roll across the ground for a certain distance before coming to a stop. We can infer by this that the energy you supplied to the football by kicking it dissipated after it rolled across the ground for a certain distance. We can conclude that there is a certain resistance against the ball as it rolls across the ground which drains its energy eventually causing it to stop due to the lack of energy. This resistive force which the ground applies on the rolling football is rolling friction.
Rolling friction is the resistive force offered by any surface which opposes the rolling motion of any object that rolls over it, thus causing it to slow down and eventually stop. Rolling friction occurs when a spherical or round object rolls across a surface. Rolling friction is also sometimes called rolling drag or rolling resistance.

Differences between rolling and sliding friction:

When a spherical or round body rolls across the surface of across a surface, the resistance in motion which arises is rolling friction.

On the other hand, when an object with a flat side slides across a surface, the resistance in motion which arises is sliding friction.

It is much easier to roll an object than to slide the same object. When a spherical or round object rolls, it has only a part of its surface in contact with the ground, thus there is less resistance offered by the ground towards it. But when an object with a flat side slides across the surface, all of that side is in contact with the ground, and it bears maximum resistance from the ground. A simple example for this difference is the gas cylinder; it is difficult to slide a gas cylinder across the floor, but it is easier to tilt the cylinder to the side and roll it across the floor. Not only it is easier to roll an object over sliding it, but it is also faster and more convenient. Thus, objects like stands, furniture, and bigger decorations have tiny wheels under them sometimes; this makes it easier to move it around.

Other than this, the coefficient of rolling friction is smaller than the coefficient of sliding friction under the same conditions.

The formula to calculate rolling friction:

The general equation to calculate rolling friction is,
               Fr = μrN
Fris the rolling friction, or the resistance towards rolling objects,
μris the coefficient of rolling friction,
N is the normal reaction on the object
μr, which is the coefficient of rolling frictions can be defined as the ratio of the force of the rolling friction to the total weight of the object.

Rolling resistance can also be expressed as,
               Fr = μrW
Fris the rolling friction, or the resistance towards rolling objects,
μr is the coefficient of rolling friction,
W is the weight of the object,

Some typical coefficients of rolling friction:

Following are some typical coefficients of rolling friction we come across in our everyday life.

Everyday usage scenariosRolling Resistance Coefficients
Railroad steel wheels on steel rails0.001 – 0.002
Bicycle tire on the wooden track0.001
Low resistance tubeless tires0.002 – 0.005
Bicycle tire on concrete0.002
Bicycle tire on asphalt0.004
Dirty tram rails0.005
The truck tire on asphalt0.006 – 0.01
Bicycle tire on a roughly paved road0.008
Ordinary car tires on concrete and new asphalt0.01 – 0.015
Car tires on tar or asphalt0.02
Car tires on gravel0.02
Car tires on cobbles0.03
Car tires on solid sand0.04 – 0.08
Car tires on loose sand0.2 – 0.4

Factors that influence rolling friction:

There are many factors that subtly influence rolling friction, like the shape of the wheel, type of surfaces, speed of the wheel and pressure on the wheel.

Among these many tiny factors, the factors that directly influence the friction and inhibit motion are:

1. Elastic Deformations
2. Surface Irregularities
3. Molecular Friction

  • 1) Elastic Deformations: Materials like rubbers which are popularly used to make tires deform when pressure is applied to them. But we may not observe that even hard materials like asphalt or concrete deform slightly when pressure is applied to them, by the weight of something like a car which goes over them. These deformations which are in contact are the major factors inhibiting motion. Material choosing is important precisely due to this reason. If the wheels of a car are made up of steel or iron which have lesser potential to deform, not considering the added weight, it becomes much more difficult to control the car. Rubber tires filled with air are used to have the best control of the car.

  • 2)Surface Irregularities: The surface of the entire wheel and the surface of the ground come into contact when the wheel is spinning. But the road will never be completely even. The wheel too will not be perfectly even. There will be irregularities on both the surfaces. This roughness of the surface is a reason for resistance. Gears and roller bearings are polished to prevent surface irregularities and reduce friction. On the other hand, grooves are added to tires to increase friction and thus give better control and braking.

  • 3) Molecular Friction: Molecular friction is caused by the molecular attraction or molecular adhesion between the materials used to make the wheel or any other rolling object and the surface on which the object travels. This is the reason why the materials used to construct the wheel and surface is important. This molecular friction can be viewed as a kind of “stickiness” factor between the material of the wheel and material of the surface on which the wheel travels. When some materials are pushed together, molecular force tries to keep them together and prevents them from being pulled apart. For example, if you roll a highly polished metal ball over materials like rubber in the form of a sheet, you can see that the metal ball does not really roll well as it slightly sticks to the rubber sheet. This can be thought of a wheel with glue applied to it rolling across a surface. This applies only to specific materials.