rolling friction


Friction is the force resisting the relative motion of two surfaces in contact or a surface in contact with a fluid (e.g. air on an aircraft or water in a pipe). It is not a fundamental force, as it is derived from electromagnetic forces between atoms and electrons, and so cannot be calculated from first principles, but instead must be found empirically. When contacting surfaces move relative to each other, the friction between the two objects converts kinetic energy into thermal energy, or heat. Friction between solid objects is often referred to as dry friction or sliding friction and between a solid and a gas or liquid as fluid friction. Both of these types of friction are called kinetic friction. Contrary to many popular explanations, sliding friction is caused not by surface roughness but by chemical bonding between the surfaces. Surface roughness and contact area, however, do affect sliding friction for micro- and nano-scale objects where surface area forces dominate inertial forces. Internal friction is the motion-resisting force between the surfaces of the particles making up the substance. Friction should not be confused with traction. Surface area does not affect friction significantly because as contact area increases, force per unit area decreases. However, in traction surface area is essential.

Coulomb friction

Coulomb friction, named after Charles-Augustin de Coulomb, is a model to describe friction forces. It is described by the equation:

F_mathrm{f} = mu F_mathrm{n}


  • F_mathrm{f} is either the force exerted by friction, or, in the case of equality, the maximum possible magnitude of this force.
  • mu is the coefficient of friction, which is an empirical property of the contacting materials,
  • F_mathrm{n} is the normal force exerted between the surfaces.

For surfaces at rest relative to each other mu = mu_mathrm{s}, where mu_mathrm{s} is the coefficient of static friction. This is usually larger than its kinetic counterpart. The Coulomb friction may take any value from zero up to F_mathrm{f}, and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence.

For surfaces in relative motion mu = mu_mathrm{k}, where mu_mathrm{k} is the coefficient of kinetic friction. The Coulomb friction is equal to F_mathrm{f}, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.

This approximation mathematically follows from the assumptions that surfaces are in atomically close contact only over a small fraction of their overall area, that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact), and that frictional force is proportional to the applied normal force, independently of the contact area (you can see the experiments on friction from Leonardo Da Vinci). Such reasoning aside, however, the approximation is fundamentally an empirical construction. It is a rule of thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility – though in general the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.

Coefficient of friction

The coefficient of friction (also known as the frictional coefficient) is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction (the two materials slide past each other easily), while rubber on pavement has a high coefficient of friction (the materials do not slide past each other easily). Coefficients of friction range from near zero to greater than one – under good conditions, a tire on concrete may have a coefficient of friction of 1.7.

When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, Scotch tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive in this way.

The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.

The coefficient of friction is an empirical measurement – it has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but Teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property – even Magnetic levitation vehicles have drag. Rubber in contact with other surfaces can yield friction coefficients from 1.0 to 2.

Static friction

Static friction is a force between two objects that are not moving relative to each other. For example, static friction can prevent an object from sliding down a sloped surface. The coefficient of static friction, typically denoted as μs, is usually higher than the coefficient of kinetic friction. The initial force to get an object moving is often dominated by static friction.

Another important example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction.

The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction, although this term is not used universally. The value is given by the product of the normal force and coefficient of static friction.

Kinetic friction

Kinetic (or dynamic) friction occurs when two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as μk, and is usually less than the coefficient of static friction.

Examples of kinetic friction:

  • Sliding friction (also called dry friction) is when two objects are rubbing against each other. Putting a book flat on a desk and moving it around is an example of sliding friction.
  • Fluid friction is the interaction between a solid object and a fluid (liquid or gas), as the object moves through the fluid. The drag of air on an airplane or of water on a swimmer are two examples of fluid friction. This kind of friction is not only due to rubbing, which generates a force tangent to the surface of the object (such as sliding friction). It is also due to forces that are orthogonal to the surface of the object. These orthogonal forces significantly (and mainly, if relative velocity is high enough) contribute to fluid friction. Fluid friction is the classic name of this force. This name is no longer used in modern fluid dynamics. Since rubbing is not its only cause, in modern fluid dynamics the same force is typically referred to as drag or fluid resistance, while the force component due to rubbing is called skin friction. Notice that a fluid can in some cases exert, together with drag, a force orthogonal to the direction of the relative motion of the object (lift). The net force exerted by a fluid (drag + lift) is called fluidodynamic force (aerodynamic if the fluid is a gas, or idrodynamic is the fluid is a liquid).

Other types of friction

Rolling resistance

Rolling resistance is the force that resists the rolling of a wheel or other circular objects along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. Typical values for the coefficient of rolling resistance are 0.001. One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products.

Triboelectric effect

Rubbing dissimilar materials against one another can cause a build-up of electrostatic charge, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges, explosions can be caused by ignition of the flammable mixture.

Reducing friction


Devices such as tires, ball bearings, air cushion or roller bearing can change sliding friction into a much smaller type of rolling friction. Many thermoplastic materials such as nylon, HDPE and PTFE are commonly used for low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load.


A common way to reduce friction is by using a lubricant, such as oil, water, or grease, which is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called tribology. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives.

Superlubricity, a recently-discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated.

Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and talc; acoustic lubrication actually uses sound as a lubricant.

Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as dither.

Energy of friction

According to the law of conservation of energy, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into heat. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat. Since heat quickly dissipates, many early philosophers, including Aristotle, wrongly concluded that moving objects lose energy without a driving force.

When an object is pushed along a surface, the energy converted to heat is given by:

E_{th} = mu_mathrm{k} int F_mathrm{n}(x) dx,
Fn is the normal force,
μk is the coefficient of kinetic friction,
x is the coordinate along which the object transverses.
Physical wear is associated with friction. While this can be beneficial, as in polishing, it is often a problem. As materials are worn away, fit and finish of a object can degrade until it no longer functions properly.

Work of friction

In the reference frame of the interface between two surfaces, static friction always does no work, because there is never any displacement. In the same reference frame, kinetic friction is always in the direction opposite the motion and so does negative work. However, friction can do positive work in certain inertial frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the floor, an inertial frame of reference. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing positive work.

The work done by friction can translate into deformation, wear, and heat that can affect the contact surface's material properties (and even the coefficient of friction itself). The work done by friction can also be used to mix materials such as in the technique of friction welding.

See also


External links

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