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were made by Leonardo da Vinci as early as 1493 when he documented the classic laws of sliding friction in his unpublished notebook.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 that resists motion between two surfaces that are sliding against each other. There are various kinds of friction. And one among them 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 that 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.
In this chapter, you will learn the following concepts -
Rolling friction - An introduction
Differences Between Rolling and Sliding Friction:
Formula of Rolling Friction
Coefficients of Rolling Friction
Factors Influencing Rolling Friction
Frequently asked question
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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 them 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
where:
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
where:
Fris the rolling friction, or the resistance towards rolling objects,
μr is the coefficient of rolling friction,
W is the weight of the object,
Following are some typical coefficients of rolling friction we come across in our everyday life.
Some Typical Coefficients of Rolling Friction:
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
Elastic Deformations
Surface Irregularities
Molecular Friction
Elastic Deformations: Materials like rubbers 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.
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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 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.
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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 the 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 as a wheel with glue applied to it rolling across a surface. This applies only to specific materials.
FAQs on Rolling Friction
1. What is rolling friction as explained in Physics?
Rolling friction is the resistive force that acts on a body when it rolls over a surface, opposing its motion. This force arises primarily because of the deformation of both the rolling object and the surface at the point of contact. Unlike sliding friction, it involves a continuous process of deformation and restoration, which causes energy loss and slows the object down. It is also referred to as rolling resistance or rolling drag.
2. What is the formula used to calculate rolling friction?
The formula to calculate the force of rolling friction (Fr) is given by:
Fr = μr * N
Where:
- Fr is the force of rolling friction.
- μr is the coefficient of rolling friction, a value that depends on the materials of the object and the surface.
- N is the normal force, which is the force exerted by the surface on the object, perpendicular to the surface. For an object on a horizontal surface, this is equal to its weight (mg).
3. How does rolling friction compare to static and sliding friction?
For any given pair of surfaces, the magnitudes of the different types of friction generally follow this order:
Static Friction (limiting) > Sliding Friction > Rolling Friction
This is why it is much easier to roll a heavy object, like a gas cylinder or a large suitcase on wheels, than it is to slide it across the same surface. The force required to overcome rolling friction is significantly smaller than that needed to overcome sliding friction.
4. What are some real-world examples of rolling friction?
Rolling friction is a common phenomenon observed in daily life. Some key examples include:
- The wheels of a car, bicycle, or skateboard rolling on the road.
- A bowling ball rolling down the lane.
- The motion of ball bearings in machinery to reduce overall friction.
- A suitcase with wheels being pulled across an airport floor.
- A pen with a ballpoint tip rolling across paper to leave a trail of ink.
5. What are the primary causes of rolling friction at a microscopic level?
Rolling friction is not caused by surface roughness in the same way as sliding friction. Instead, its primary causes are:
- Elastic Hysteresis: When a wheel rolls, it deforms the surface slightly, creating a small depression. The wheel must constantly 'climb' out of this depression. The surface material does not perfectly spring back to its original shape instantly, resulting in a net resistive force and energy loss.
- Adhesion: At the molecular level, there can be adhesive forces between the surface of the rolling object and the surface it rolls on. Energy is required to break these temporary molecular bonds as the object rolls forward, contributing to the resistance.
6. Why is it significantly easier to roll an object than to slide it?
It is easier to roll an object because the mechanism causing resistance is fundamentally different and less energy-intensive than that of sliding. In sliding, entire surfaces grind against each other, requiring the continuous breaking of numerous microscopic welds or bonds. In rolling, the contact area is very small, and the primary resistance comes from the slight deformation of the surfaces. The energy lost in this deformation-restoration cycle is much less than the energy lost to overcoming the widespread intermolecular forces in sliding, making the coefficient of rolling friction much smaller.
7. How does the radius of a rolling wheel affect the rolling friction?
Generally, for the same load and materials, a wheel with a larger radius will experience less rolling friction. This is because a larger wheel deforms the surface less for a given load. Even if the depth of the indentation is the same, the angle of the slope the wheel has to 'climb' out of is shallower for a larger radius wheel. This results in a smaller horizontal resistive force, making it easier to roll.
8. Do factors like speed and material type influence rolling friction?
Yes, several factors influence rolling friction. The most important is the nature of the materials; softer, more deformable materials (like a soft rubber wheel on a soft carpet) will have a much higher rolling friction than hard materials (like a steel wheel on a steel rail). Additionally, speed can have an effect; at higher speeds, the deformation and recovery of the material may not keep pace, often leading to an increase in rolling resistance.
