Friction

# Friction

Overview
Friction is the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:
• Dry friction resists relative lateral motion of two solid surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

s in contact. Dry friction is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces.

• Fluid friction describes the friction between layers within a viscous fluid that are moving relative to each other.

• Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces.

• Skin friction is a component of drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

, the force resisting the motion of a solid body through a fluid.

• Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation
Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

.

When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

into heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

.
Discussion

Recent Discussions
Encyclopedia
Friction is the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:
• Dry friction resists relative lateral motion of two solid surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

s in contact. Dry friction is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces.

• Fluid friction describes the friction between layers within a viscous fluid that are moving relative to each other.

• Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces.

• Skin friction is a component of drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

, the force resisting the motion of a solid body through a fluid.

• Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation
Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

.

When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

into heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear
Wear
In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface....

, which may lead to performance degradation and/or damage to components. Friction is a component of the science of tribology
Tribology
Tribology is the science and engineering of interacting surfaces in relative motion. It includes the study and application of the principles of friction, lubrication and wear...

.

Friction is not a fundamental force but occurs because of the electromagnetic forces between charged particles which constitute the surfaces in contact. Because of the complexity of these interactions friction cannot be calculated from first principles, but instead must be found empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

ly.

## History

The classic rules of sliding friction were discovered by Leonardo da Vinci
Leonardo da Vinci
Leonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...

(1452-1519), but remained unpublished in his notebooks. They were rediscovered by Guillaume Amontons
Guillaume Amontons
Guillaume Amontons was a French scientific instrument inventor and physicist. He was one of the pioneers in tribology, apart from Leonardo da Vinci, John Theophilus Desaguliers, Leonard Euler and Charles-Augustin de Coulomb.-Life:Guillaume was born in Paris, France. His father was a lawyer from...

(1699) and were further developed by Charles-Augustin de Coulomb
Charles-Augustin de Coulomb
Charles-Augustin de Coulomb was a French physicist. He is best known for developing Coulomb's law, the definition of the electrostatic force of attraction and repulsion. The [SI unit] of charge, the coulomb, was named after him....

(1785). Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...

(1707-1783) derived the angle of repose
Angle of repose
The angle of repose or, more precisely, the critical angle of repose, of a granular material is the steepest angle of descent or dip of the slope relative to the horizontal plane when material on the slope face is on the verge of sliding. This angle is in the range 0°–90°.When bulk granular...

of a weight on an inclined plane and first distinguished between static and kinetic friction. Arthur Morrin (1833) developed the concept of static friction. Osborne Reynolds
Osborne Reynolds
Osborne Reynolds FRS was a prominent innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design.-Life:...

(1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering.

The focus of research during the last century has been to understand the physical mechanisms behind friction. F. Phillip Bowden and David Tabor
David Tabor
David Tabor was a British physicist who coined the word tribology for the study of frictional interaction between surfaces.He was Professor of Physics in the University of Cambridge, then Emeritus professor...

(1950) showed that at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by "asperities" (roughness) increases with pressure, explaining the proportionality between normal force and frictional force. The development of the atomic force microscope
Atomic force microscope
Atomic force microscopy or scanning force microscopy is a very high-resolution type of scanning probe microscopy, with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit...

(1986) has recently enabled scientists to study friction at the atomic scale.

## Laws of dry friction

The elementary properties of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws:
• Amontons' First Law: The force of friction is directly proportional to the applied load.
• Amontons' Second Law: The force of friction is independent of the apparent area of contact.
• Coulomb's Law of Friction: Kinetic friction is independent of the sliding velocity.

Amontons' 2nd Law is an idealization assuming perfectly rigid and inelastic materials. For example, wider tires on cars provide more traction than narrow tires for a given vehicle mass because of surface deformation of the tire.

## Dry friction

Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are static friction between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces.

Coulomb friction, named after Charles-Augustin de Coulomb, is an approximate model used to calculate the force of dry friction. It is governed by the equation:

where
• is the force of friction exerted by each surface on the other. It is parallel to the surface, in a direction opposite to the net applied force.
• is the coefficient of friction, which is an empirical property of the contacting materials,
• is the normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

exerted by each surface on the other, directed perpendicular (normal) to the surface.

The Coulomb friction may take any value from zero up to , 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. This maximum force is known as traction
Traction (engineering)
Traction refers to the maximum frictional force that can be produced between surfaces without slipping.The units of traction are those of force, or if expressed as a coefficient of traction a ratio.-Traction:...

.

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
Curling
Curling is a sport in which players slide stones across a sheet of ice towards a target area. It is related to bowls, boule and shuffleboard. Two teams, each of four players, take turns sliding heavy, polished granite stones, also called "rocks", across the ice curling sheet towards the house, a...

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 normal force

The normal force is defined as the net force compressing two parallel surfaces together; and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where . In this case, the magnitude of the friction force is the product of the mass of the object, the acceleration due to gravity, and the coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends only on the material. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence the mass of the block.

If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal force between the object and the surface is just its weight, which is equal to its mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

multiplied by the acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

due to earth's gravity, g
Standard gravity
Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...

. If the object is on a tilted surface such as an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane. Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis, usually via a free body diagram
Free body diagram
A free body diagram, also called a force diagram, is a pictorial representation often used by physicists and engineers to analyze the forces acting on a body of interest. A free body diagram shows all forces of all types acting on this body. Drawing such a diagram can aid in solving for the unknown...

. Depending on the situation, the calculation of the normal force may include forces other than gravity.

### Coefficient of friction

The 'coefficient of friction' (COF), also known as a 'frictional coefficient' or 'friction coefficient' and symbolized by the Greek letter µ
Mu (letter)
Carlos Alberto Vives Restrepo is a Grammy Award and three-time Latin Grammy Award winning-Colombian singer, composer and actor.-Biography:...

, is a dimensionless
Dimensionless quantity
In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

scalar
Scalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...

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, while rubber on pavement has a high coefficient of friction. 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.

For surfaces at rest relative to each other , where is the coefficient of static friction. This is usually larger than its kinetic counterpart.

For surfaces in relative motion , where is the coefficient of kinetic friction. The Coulomb friction is equal to , and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.

It was Arthur-Jules Morin
Arthur Morin
Arthur Jules Morin was a French physicist. He conducted experiments in mechanics and invented the Morin dynamometer....

who introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

– it has to be measured experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

ally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is usually larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon.

Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon
Polytetrafluoroethylene
Polytetrafluoroethylene is a synthetic fluoropolymer of tetrafluoroethylene that finds numerous applications. PTFE is most well known by the DuPont brand name 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
Magnetic levitation
Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields...

vehicles
Maglev train
Maglev , is a system of transportation that uses magnetic levitation to suspend, guide and propel vehicles from magnets rather than using mechanical methods, such as friction-reliant wheels, axles and bearings...

have drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that µ is always < 1, but this is not true. While in most relevant applications µ < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, silicone rubber
Silicone rubber
Silicone rubber is an elastomer composed of silicone—itself a polymer—containing silicon together with carbon, hydrogen, and oxygen. Silicone rubbers are widely used in industry, and there are multiple formulations...

or acrylic rubber
Acrylic rubber
Acrylic rubber, known by the chemical name alkyl acrylate copolymer or the tradename Hytemp, is a type of rubber that has outstanding resistance to hot oil and oxidation. It has a continuous working temperature of and an intermittent limit of . Its disadvantage is its low resistance to moisture,...

-coated surfaces have a coefficient of friction that can be substantially larger than 1.

While it is often stated that the COF is a "material property," it is better categorized as a "system property." Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...

and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials. For example, a copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test.

#### Approximate coefficients of friction

Materials BAM
BAM (material)
BAM is a ceramic alloy created from an alloy of boron, aluminium and magnesium and titanium boride . It is one of the hardest known materials, after diamond and cubic boron nitride...

(for the elements boron, aluminium, and magnesium), has an approximate coefficient of friction of 0.02, about half that of PTFE. Under certain special conditions some materials have even lower friction coefficients. An example is (highly ordered pyrolytic) graphite, of which the coefficient can drop below 0.01.
This regime is also called superlubricity
Superlubricity
Superlubricity is a regime of motion in which friction vanishes or very nearly vanishes.Superlubricity may occur when two crystalline surfaces slide over each other in dry incommensurate contact...

.

### Static friction

Static friction is friction between two solid 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 static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: . When there is no sliding occurring, the friction force can have any value from zero up to . Any force smaller than attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than overcomes the force of static friction and causes sliding to occur. The instant sliding occurs, static friction is no longer applicable—the friction between the two surfaces is then called kinetic friction.

An 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. It is also known as traction
Traction (engineering)
Traction refers to the maximum frictional force that can be produced between surfaces without slipping.The units of traction are those of force, or if expressed as a coefficient of traction a ratio.-Traction:...

.

### 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 for the same materials. However, Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

comments that "with dry metals it is very hard to show any difference."

New models are beginning to show how kinetic friction can be greater than static friction. Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities;however, in many other cases roughness effects are dominant, for example in rubber to road friction. Surface roughness and contact area, however, do affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces.

### Angle of friction

For certain applications it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the angle of friction or friction angle. It is defined as:

where θ is the angle from vertical and µ is the static coefficient of friction between the objects. This formula can also be used to calculate µ from empirical measurements of the friction angle.

### Friction at the atomic level

Determining the forces required to move atoms past each other is a challenge in designing nanomachines. In 2008 scientists for the first time were able to move a single atom across a surface, and measure the forces required. Using ultrahigh vacuum and nearly-zero temperature (5 K), a modified atomic force microscope
Atomic force microscope
Atomic force microscopy or scanning force microscopy is a very high-resolution type of scanning probe microscopy, with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit...

was used to drag a cobalt
Cobalt
Cobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....

atom, and a carbon monoxide
Carbon monoxide
Carbon monoxide , also called carbonous oxide, is a colorless, odorless, and tasteless gas that is slightly lighter than air. It is highly toxic to humans and animals in higher quantities, although it is also produced in normal animal metabolism in low quantities, and is thought to have some normal...

molecule, across surfaces of copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

and platinum
Platinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

.

### Limitations of the Coulomb model

The Coulomb 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
Contact area
When two objects touch, a certain portion of their surface areas will be in contact with each other. Contact area is the fraction of this area that consists of the atoms of one object in contact with the atoms of the other object...

is proportional to the normal force (until saturation
Saturated model
In mathematical logic, and particularly in its subfield model theory, a saturated model M is one which realizes as many complete types as may be "reasonably expected" given its size...

, 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.

When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, adhesive tape
Adhesive tape is one of many varieties of backing materials coated with an adhesive. Several types of adhesives can be used.-Types:Pressure sensitive 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
Drag racing
Drag racing is a competition in which specially prepared automobiles or motorcycles compete two at a time to be the first to cross a set finish line, from a standing start, in a straight line, over a measured distance, most commonly a ¼-mile straight track....

tires are adhesive in this way. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.

### Numerical simulation of the Coulomb model

Despite being a simplified model of friction, the Coulomb model is useful in many numerical simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...

applications such as multibody system
Multibody system
A multibody system is used to model the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements.- Introduction :...

s and granular material
Granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact . The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations...

. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...

mechanical systems with Coulomb friction and bilateral and/or unilateral contact. Some quite nonlinear effects, such as the so-called Painlevé paradox
The Painlevé paradox is a well known example by Paul Painlevé in rigid-body dynamics that showed that rigid-body dynamics with both contact friction and Coulomb friction is inconsistent. This is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in...

es, may be encountered with Coulomb friction.

### Dry friction and instabilities

Dry friction can induce several types of instabilities in mechanical systems, which display a stable behaviour in the absence of friction. For instance, friction-related dynamical instabilities are thought to be responsible of brake squeal and of the 'song' of a glass harp
Glass harp
A glass harp is an instrument made of upright wine glasses....

, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity. A connection between dry friction and flutter instability in a simple mechanical system has been discovered.

## Fluid friction

Fluid friction occurs between layers within a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

that are moving relative to each other. This internal resistance to flow is described by viscosity. In everyday terms viscosity is "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement.

All real fluids (except superfluids) have some resistance to stress and therefore are viscous, but a fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid.

## Lubricated friction

Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. Lubrication is a technique employed to reduce wear of one or both surfaces in close proximity moving relative to each another by interposing a substance called a lubricant between the surfaces.

In most cases the applied load is carried by pressure generated within the fluid due to the frictional viscous resistance to motion of the lubricating fluid between the surfaces. Adequate lubrication allows smooth continuous operation of equipment, with only mild wear, and without excessive stresses or seizures at bearings. When lubrication breaks down, metal or other components can rub destructively over each other, causing heat and possibly damage or failure.

## Skin friction

Skin friction arises from the friction of the fluid against the "skin" of the object that is moving through it. Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the area of the surface of the body that is in contact with the fluid. Skin friction follows the drag equation
Drag equation
In fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid....

and rises with the square of the velocity.

Skin friction is caused by viscous drag in the boundary layer
Boundary layer
In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

around the object. There are two ways to decrease skin friction: the first is to shape the moving body so that smooth flow is possible, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as is practicable.

## Internal friction

Internal friction is the force resisting motion between the elements making up a solid material while it undergoes plastic deformation.

Plastic deformation in solids is an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) an applied force or a change in temperature. The change of an object's shape is called strain
Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

. The force causing it is called stress. Stress does not necessarily cause permanent change. As deformation occurs, internal forces oppose the applied force. If the applied stress is not too large these opposing forces may completely resist the applied force, allowing the object to assume a new equilibrium state and to return to its original shape when the force is removed. This is what is known in the literature as elastic deformation (or elasticity). Larger forces in excess of the elastic limit may cause a permanent (irreversible) deformation of the object. This is what is known as plastic deformation.

### Rolling resistance

Rolling resistance is the force that resists the rolling of a wheel or other circular object 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
Motor vehicle
A motor vehicle or road vehicle is a self-propelled wheeled vehicle that does not operate on rails, such as trains or trolleys. The vehicle propulsion is provided by an engine or motor, usually by an internal combustion engine, or an electric motor, or some combination of the two, such as hybrid...

tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

A road is a thoroughfare, route, or way on land between two places, which typically has been paved or otherwise improved to allow travel by some conveyance, including a horse, cart, or motor vehicle. Roads consist of one, or sometimes two, roadways each with one or more lanes and also any...

, a process which generates heat and sound
Roadway noise is the collective sound energy emanating from motor vehicles. In the USA it contributes more to environmental noise exposure than any other noise source, and is constituted chiefly of engine, tire, aerodynamic and braking elements...

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, explosion
Explosion
An explosion is a rapid increase in volume and release of energy in an extreme manner, usually with the generation of high temperatures and the release of gases. An explosion creates a shock wave. If the shock wave is a supersonic detonation, then the source of the blast is called a "high explosive"...

s can be caused by ignition of the flammable mixture.

### Belt friction

Belt friction is a physical property observed from the forces acting on a belt wrapped around a pulley, when one end is being pulled. The resulting tension, which acts on both ends of the belt, can be modeled by the belt friction equation.

In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.

### Devices

Devices such as wheels, ball bearing
Ball bearing
A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races.The purpose of a ball bearing is to reduce rotational friction and support radial and axial loads. It achieves this by using at least two races to contain the balls and transmit...

s, roller bearings, and air cushion or other types of fluid bearing
Fluid bearing
Fluid bearings are bearings which support the bearing's loads solely on a thin layer of liquid or gas.They can be broadly classified as fluid dynamic bearings or hydrostatic bearings. Hydrostatic bearings are externally pressurized fluid bearings, where the fluid is usually oil, water or air, and...

s can change sliding friction into a much smaller type of rolling friction.

Many thermoplastic
Thermoplastic
Thermoplastic, also known as a thermosoftening plastic, is a polymer that turns to a liquid when heated and freezes to a very glassy state when cooled sufficiently...

materials such as nylon
Nylon
Nylon is a generic designation for a family of synthetic polymers known generically as polyamides, first produced on February 28, 1935, by Wallace Carothers at DuPont's research facility at the DuPont Experimental Station...

, HDPE and PTFE are commonly used in low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load. For improved wear
Wear
In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface....

resistance, very high molecular weight grades are usually specified for heavy duty or critical bearings.

### Lubricants

A common way to reduce friction is by using a lubricant
Lubricant
A lubricant is a substance introduced to reduce friction between moving surfaces. It may also have the function of transporting foreign particles and of distributing heat...

, 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
Tribology
Tribology is the science and engineering of interacting surfaces in relative motion. It includes the study and application of the principles of friction, lubrication and wear...

. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives.

Superlubricity
Superlubricity
Superlubricity is a regime of motion in which friction vanishes or very nearly vanishes.Superlubricity may occur when two crystalline surfaces slide over each other in dry incommensurate contact...

, a recently-discovered effect, has been observed in graphite
Graphite
The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Ancient Greek γράφω , "to draw/write", for its use in pencils, where it is commonly called lead . Unlike diamond , graphite is an electrical conductor, a semimetal...

: 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
Talc
Talc is a mineral composed of hydrated magnesium silicate with the chemical formula H2Mg34 or Mg3Si4O102. In loose form, it is the widely-used substance known as talcum powder. It occurs as foliated to fibrous masses, its crystals being so rare as to be almost unknown...

; acoustic lubrication
Acoustic lubrication
Acoustic or sonic lubrication occurs when sound permits vibration to introduce separation between the sliding faces. This could happen between two plates or between a series of particles...

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
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

, 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
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

, 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:

where
is the normal force,
is the coefficient of kinetic friction,
is the coordinate along which the object transverses.

Energy lost to a system as a result of friction is a classic example of thermodynamic irreversibility
Irreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....

.

### Work of friction

In the reference frame of the interface between two surfaces, static friction does no work
Mechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...

, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does negative work. However, friction can do positive work in certain frames of reference
Frames of Reference
Frames of Reference is a 1960 educational film by Physical Sciences Study Committee.The film was made to be shown in high school physics courses. In the film University of Toronto physics professors Patterson Hume and Donald Ivey explain the distinction between inertial and nonintertial frames of...

. 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 frame of reference in which the floor is stationary. 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
Wear
In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface....

, and heat that can affect the contact surface properties (even the coefficient of friction between the surfaces). This can be beneficial as in polishing
Polishing
Polishing is the process of creating a smooth and shiny surface by rubbing it or using a chemical action, leaving a surface with a significant specular reflection In some materials polishing is also able to reduce diffuse reflection to...

. The work of friction is used to mix and join materials such as in the process of friction welding
Friction welding
Friction welding is a class of solid-state welding processes that generates heat through mechanical friction between a moving workpiece and a stationary component, with the addition of a lateral force called "upset" to plastically displace and fuse the materials...

. Excessive erosion or wear of mating surfaces occur when work due frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces (fretting
Fretting
Fretting refers to wear and sometimes corrosion damage at the asperities of contact surfaces. This damage is induced under load and in the presence of repeated relative surface motion, as induced for example by vibration...

) exacerbates wear of frictional forces. Bearing seizure or failure may result from excessive wear due to work of friction. As surfaces are worn by work due to friction, fit
Tolerance (engineering)
Engineering tolerance is the permissible limit or limits of variation in# a physical dimension,# a measured value or physical property of a material, manufactured object, system, or service,# other measured values ....

and surface finish of an object may degrade until it no longer functions properly.

### Transportation

The term adhesion railway or adhesion traction describes the most common type of railway, where power is applied by driving some or all of the wheels of the locomotive. Thus, it relies on the friction between a steel wheel and a steel rail. Note that steam locomotives of old were driven only by...

refers to the grip wheels of a train have on the rails.
Road slipperiness or skid resistance is the technical term for the cumulative effects of snow, ice, water, loose material and the road surface on the traction produced by the wheels of a vehicle...

is an important design and safety factor for automobiles
• Split friction
Split friction
A special road safety problem is Split friction or μ - split; when the friction significantly differs between the left and the right wheelpath. The road may then not be perceived as hazardous when accelerating, cruising or even braking softly. But in a case of hard braking, the car will start to...

is a particularly dangerous condition arising due to varying friction on either side of a car.
Road surface texture are deviations from a planar surface, affecting the vehicle/tyre interaction. Pavement texture is divided into:* Microtexture with wavelengths from 0 mm up to 0.5 mm* Macrotexture with wavelengths from 0.5 mm up to 50 mm...

affects the interaction of tires and the driving surface.

### Measurement

• A tribometer
Tribometer
A tribometer is an instrument that measures tribological quantities, such as coefficient of friction, friction force, and wear volume, between two surfaces in contact...

is an instrument that measures friction on a surface.
• A profilograph
Profilograph
The profilograph is a device used to measure pavement surface roughness. In the early 20th century, Profilographs were low speed rolling devices. Today many Profilographs are advanced high speed systems with a laserbased height sensor in combination with a inertial system that creates a large...

is a device used to measure pavement surface roughness.

• Angle of repose
Angle of repose
The angle of repose or, more precisely, the critical angle of repose, of a granular material is the steepest angle of descent or dip of the slope relative to the horizontal plane when material on the slope face is on the verge of sliding. This angle is in the range 0°–90°.When bulk granular...

• Contact dynamics
Contact dynamics
Contact dynamics deals with the motion of multibody systems subjected to unilateral contacts and friction. Such systems are omnipresent in many multibody dynamics applications...

• Contact mechanics
Contact mechanics
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The physical and mathematical formulation of the subject is built upon the mechanics of materials and continuum mechanics and focuses on computations involving elastic, viscoelastic, and plastic...

• Drag (physics)
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

In railroad engineering, the factor of adhesion of a locomotive is the weight on the driving wheels divided by the starting tractive effort.A common rule is that for a steam locomotive a good factor of adhesion equals or exceeds 4, but not by too much...

• Friction welding
Friction welding
Friction welding is a class of solid-state welding processes that generates heat through mechanical friction between a moving workpiece and a stationary component, with the addition of a lateral force called "upset" to plastically displace and fuse the materials...

• Frictionless plane
Frictionless plane
The frictionless plane is a concept from the writings of Galileo Galilei. In his 1608 The Two New Sciences, Galileo presented a formula that predicted the motion of an object moving down an inclined plane. His formula was based upon his past experimentation with free-falling bodies...

• Non-smooth mechanics
Non-smooth mechanics
Non-smooth mechanics is a modeling approach in mechanics which does not require the time evolutions of the positions and of the velocities to be smooth functions anymore. Due to possible impacts, the velocities of the mechanical system are even allowed to undergo jumps at certain time instants in...

• Stick-slip phenomenon
Stick-slip phenomenon
The stick-slip phenomenon, also known as the slip-stick phenomenon or simply stick-slip, is the spontaneous jerking motion that can occur while two objects are sliding over each other.- Cause :...

• Tire
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

• Traction (engineering)
Traction (engineering)
Traction refers to the maximum frictional force that can be produced between surfaces without slipping.The units of traction are those of force, or if expressed as a coefficient of traction a ratio.-Traction:...

Transient friction loading, also known as TFL, is the mechanical stress induced on an object due to transient or vibrational frictional forces.-Examples:...

• Triboelectric effect
Triboelectric effect
The triboelectric effect is a type of contact electrification in which certain materials become electrically charged after they come into contact with another different material and are then separated...

• Tribology
Tribology
Tribology is the science and engineering of interacting surfaces in relative motion. It includes the study and application of the principles of friction, lubrication and wear...

• Tribometer
Tribometer
A tribometer is an instrument that measures tribological quantities, such as coefficient of friction, friction force, and wear volume, between two surfaces in contact...

• Unilateral contact
Unilateral contact
In mechanics, a unilateral contact denotes a mechanical constraint which prevents penetration between two bodies; see figure 1a. These bodies may be rigid or flexible...

• Wear
Wear
In materials science, wear is erosion or sideways displacement of material from its "derivative" and original position on a solid surface performed by the action of another surface....

• Galling
Galling
Galling usually refers to the adhesive wear and transfer of material between metallic surfaces in relative converging contact during sheet metal forming and other industrial operations....