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Friction is the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into ''static friction'' (" stiction") between non-moving surfaces, and ''kinetic friction'' between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1). *Fluid friction describes the friction between layers of a
viscous The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the in ...
fluid that are moving relative to each other. *Lubricated friction is a case of fluid friction where a
lubricant A lubricant (sometimes shortened to lube) is a substance that helps to reduce friction between surfaces in mutual contact, which ultimately reduces the heat generated when the surfaces move. It may also have the function of transmitting forces, t ...
fluid separates two solid surfaces. *Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. *Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation. When surfaces in contact move relative to each other, the friction between the two surfaces converts
kinetic energy In physics, the kinetic energy of an object is the energy that 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 acce ...
into
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, de ...
(that is, it converts work to
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
). 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 thermal energy whenever motion with friction occurs, for example when a
viscous The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the in ...
fluid is stirred. Another important consequence of many types of friction can be
wear Wear is the damaging, gradual removal or deformation of material at solid surfaces. Causes of wear can be mechanical (e.g., erosion) or chemical (e.g., corrosion). The study of wear and related processes is referred to as tribology. Wear in ...
, which may lead to performance degradation or damage to components. Friction is a component of the science of
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. Tribology is highly interdisciplinary, drawing on many academic fi ...
. Friction is desirable and important in supplying traction to facilitate motion on land. Most
land vehicle A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), wat ...
s rely on friction for acceleration, deceleration and changing direction. Sudden reductions in traction can cause loss of control and accidents. Friction is not itself a fundamental force. Dry friction arises from a combination of inter-surface adhesion, surface roughness, surface deformation, and surface contamination. The complexity of these interactions makes the calculation of friction from first principles impractical and necessitates the use of
empirical method Empirical research is research using empirical evidence. It is also a way of gaining knowledge by means of direct and indirect observation or experience. Empiricism values some research more than other kinds. Empirical evidence (the record of one ...
s for analysis and the development of theory. Friction is a non-conservative force – work done against friction is path dependent. In the presence of friction, some kinetic energy is always transformed to thermal energy, so
mechanical energy In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is ...
is not conserved.


History

The Greeks, including
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
,
Vitruvius Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled '' De architectura''. He originated the idea that all buildings should have three attribut ...
, and
Pliny the Elder Gaius Plinius Secundus (AD 23/2479), called Pliny the Elder (), was a Roman author, naturalist and natural philosopher, and naval and army commander of the early Roman Empire, and a friend of the emperor Vespasian. He wrote the encyclopedic ' ...
, were interested in the cause and mitigation of friction. They were aware of differences between static and kinetic friction with
Themistius Themistius ( grc-gre, Θεμίστιος ; 317 – c. 388 AD), nicknamed Euphrades, (eloquent), was a statesman, rhetorician, and philosopher. He flourished in the reigns of Constantius II, Julian, Jovian, Valens, Gratian, and Theodosius I; ...
stating in 350 that "it is easier to further the motion of a moving body than to move a body at rest". The classic laws of sliding friction were discovered by
Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested on ...
in 1493, a pioneer in
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. Tribology is highly interdisciplinary, drawing on many academic fi ...
, but the laws documented in his notebooks were not published and remained unknown. These laws were rediscovered by
Guillaume Amontons Guillaume Amontons (31 August 1663 – 11 October 1705) was a French scientific instrument inventor and physicist. He was one of the pioneers in studying the problem of friction, which is the resistance to motion when bodies make contact. He is ...
in 1699 and became known as Amonton's three laws of dry friction. Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together. This view was further elaborated by
Bernard Forest de Bélidor Bernard Forest de Bélidor (1698, Catalonia, Spain – 8 September 1761, Paris, France) was a French engineer, significant to the development of the science of hydraulics and ballistics. He was the son of Jean Baptiste Foret de Belidor, an offi ...
and
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries ...
(1750), who derived the
angle of repose The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope fac ...
of a weight on an inclined plane and first distinguished between static and kinetic friction.
John Theophilus Desaguliers John Theophilus Desaguliers FRS (12 March 1683 – 29 February 1744) was a British natural philosopher, clergyman, engineer and freemason who was elected to the Royal Society in 1714 as experimental assistant to Isaac Newton. He had studied at ...
(1734) first recognized the role of
adhesion Adhesion is the tendency of dissimilar particles or surfaces to cling to one another ( cohesion refers to the tendency of similar or identical particles/surfaces to cling to one another). The forces that cause adhesion and cohesion can ...
in friction. Microscopic forces cause surfaces to stick together; he proposed that friction was the force necessary to tear the adhering surfaces apart. The understanding of friction was further developed by
Charles-Augustin de Coulomb Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attra ...
(1785). Coulomb investigated the influence of four main factors on friction: the nature of the materials in contact and their surface coatings; the extent of the surface area; the normal pressure (or load); and the length of time that the surfaces remained in contact (time of repose). Coulomb further considered the influence of sliding velocity, temperature and humidity, in order to decide between the different explanations on the nature of friction that had been proposed. The distinction between static and dynamic friction is made in Coulomb's friction law (see below), although this distinction was already drawn by Johann Andreas von Segner in 1758. The effect of the time of repose was explained by Pieter van Musschenbroek (1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases. John Leslie (1766–1832) noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities, why then isn't it balanced through descending the opposite slope? Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion. In Leslie's view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before. Arthur Jules Morin (1833) developed the concept of sliding versus rolling friction. Osborne Reynolds (1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering. In 1877, Fleeming Jenkin and J. A. Ewing investigated the continuity between static and kinetic friction. The focus of research during the 20th century has been to understand the physical mechanisms behind friction.
Frank Philip Bowden Frank Philip Bowden CBE FRS (2 May 1903 – 3 September 1968) was an Australian physicist. Early life He was born in Hobart, Tasmania, the son of telegraph engineer Frank Prosser Bowden. Bowden received his Bachelor of Science degree fro ...
and
David Tabor David Tabor (né Tabrisky), FRS (23 October 1913 – 26 November 2005) was a British physicist who was an early pioneer of tribology, the study of frictional interaction between surfaces, and well known for his influential undergraduate textboo ...
(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 increases with pressure. The development of the
atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the op ...
(ca. 1986) enabled scientists to study friction at the
atomic scale Atomic spacing refers to the distance between the nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together. In solid materials, the ...
, showing that, on that scale, dry friction is the product of the inter-surface
shear stress Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
and the contact area. These two discoveries explain Amonton's first law ''(below)''; the macroscopic proportionality between normal force and static frictional force between dry surfaces.


Laws of dry friction

The elementary property 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.


Dry friction

Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are 'static friction' (" stiction") 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 Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attra ...
, is an approximate model used to calculate the force of dry friction. It is governed by the model: F_\mathrm \leq \mu F_\mathrm, where *F_\mathrm 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. *\mu is the coefficient of friction, which is an empirical property of the contacting materials, *F_\mathrm is the normal force exerted by each surface on the other, directed perpendicular (normal) to the surface. The Coulomb friction F_\mathrm may take any value from zero up to \mu F_\mathrm, 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. 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 is a sport in which players slide stones on a sheet of ice toward a target area which is segmented into four concentric circles. It is related to bowls, boules, and shuffleboard. Two teams, each with four players, take turns slidi ...
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.


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 N=mg\,. In this case, conditions of equilibrium tell us that the magnitude of the friction force is ''zero'', F_f = 0. In fact, the friction force always satisfies F_f\le \mu N, with equality reached only at a critical ramp angle (given by \tan^\mu) that is steep enough to initiate sliding. The friction coefficient is an
empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
(experimentally measured) structural property that depends only on various aspects of the contacting materials, such as surface roughness. The coefficient of friction is not a function of mass or volume. 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 on the mass of the block. Depending on the situation, the calculation of the normal force N might include forces other than gravity. If an object is on a level surface and subjected to an external force P tending to cause it to slide, then the normal force between the object and the surface is just N = mg + P_y, where mg is the block's weight and P_y is the downward component of the external force. Prior to sliding, this friction force is F_f = -P_x, where P_x is the horizontal component of the external force. Thus, F_f \le \mu N in general. Sliding commences only after this frictional force reaches the value F_f = \mu N. Until then, friction is whatever it needs to be to provide equilibrium, so it can be treated as simply a reaction. If the object is on a tilted surface such as an inclined plane, the normal force from gravity is smaller than mg, because less of the force of gravity is perpendicular to the face of the plane. The normal force and the frictional force are ultimately determined using vector analysis, usually via a
free body diagram A free body diagram consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it. In physics and engineering, a free body diagram (FBD; also called a force ...
. In general, process for solving any statics problem with friction is to treat contacting surfaces ''tentatively'' as immovable so that the corresponding tangential reaction force between them can be calculated. If this frictional reaction force satisfies F_f \le \mu N, then the tentative assumption was correct, and it is the actual frictional force. Otherwise, the friction force must be set equal to F_f = \mu N, and then the resulting force imbalance would then determine the acceleration associated with slipping.


Coefficient of friction

The coefficient of friction (COF), often symbolized by the Greek letter µ, is a dimensionless scalar value which equals the ratio of the force of friction between two bodies and the force pressing them together, either during or at the onset of slipping. 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. The coefficient of friction between two surfaces of similar metals is greater than that between two surfaces of different metals; for example, brass has a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum. For surfaces at rest relative to each other, \mu = \mu_\mathrm, where \mu_\mathrm is the ''coefficient of static friction''. This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and
surface roughness Surface roughness, often shortened to roughness, is a component of surface finish (surface texture). It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, ...
, both of which have their origins in the
chemical bonding A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing o ...
between atoms in each of the bulk materials and between the material surfaces and any adsorbed material. The
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...
ity of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction. For surfaces in relative motion \mu = \mu_\mathrm, where \mu_\mathrm is the ''coefficient of kinetic friction''. The Coulomb friction is equal to F_\mathrm, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.
Arthur Morin Arthur Jules Morin (19 October 1795 – 7 February 1880) was a French physicist. He conducted experiments in mechanics and invented the Morin dynamometer. He introduced the term coefficient of friction and demonstrated its utility. In 1850, he wa ...
introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an
empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
it has to be measured
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...
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 (PTFE) is a synthetic fluoropolymer of tetrafluoroethylene that has numerous applications. It is one of the best-known and widely applied PFAS. The commonly known brand name of PTFE-based composition is Teflon by Chemo ...
, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property. 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 is an elastomer (rubber-like material) 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 formulation ...
or
acrylic rubber Acrylic rubber, known by the chemical name alkyl acrylate copolymer (ACM) or the tradename HyTemp, is a type of rubber that has outstanding resistance to hot oil and oxidation. It belongs to specialty rubbers. It has a continuous working temperature ...
-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 is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
,
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
,
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...
and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials, namely surface structure. For example, a
copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pink ...
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

Under certain conditions some materials have very low friction coefficients. An example is (highly ordered pyrolytic) graphite which can have a friction coefficient below 0.01. This ultralow-friction regime is called superlubricity.


Static friction

Static friction is friction between two or more 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 ''μ''s, is usually higher than the coefficient of kinetic friction. Static friction is considered to arise as the result of surface roughness features across multiple length scales at solid surfaces. These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area. The linearity between applied load and true contact area, arising from asperity deformation, gives rise to the linearity between static frictional force and normal force, found for typical Amonton–Coulomb type 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: F_\text = \mu_\mathrm F_\text. When there is no sliding occurring, the friction force can have any value from zero up to F_\text. Any force smaller than F_\text attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than F_\text 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. However, an apparent static friction can be observed even in the case when the true static friction is zero. 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. Upon slipping, the wheel friction changes to kinetic friction. An
anti-lock braking system An anti-lock braking system (ABS) is a safety anti-skid braking system used on aircraft and on land vehicles, such as cars, motorcycles, trucks, and buses. ABS operates by preventing the wheels from locking up during braking, thereby maint ...
operates on the principle of allowing a locked wheel to resume rotating so that the car maintains static 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.


Kinetic friction

Kinetic friction, also known as dynamic friction or sliding 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 ''μ''k, and is usually less than the coefficient of static friction for the same materials. However, Richard Feynman comments that "with dry metals it is very hard to show any difference." The friction force between two surfaces after sliding begins is the product of the coefficient of kinetic friction and the normal force: F_ = \mu_\mathrm F_. This is responsible for the Coulomb damping of an oscillating or vibrating system. 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 affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces. The origin of kinetic friction at nanoscale can be explained by thermodynamics. Upon sliding, new surface forms at the back of a sliding true contact, and existing surface disappears at the front of it. Since all surfaces involve the thermodynamic surface energy, work must be spent in creating the new surface, and energy is released as heat in removing the surface. Thus, a force is required to move the back of the contact, and frictional heat is released at the front.


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: \tan = \mu_\mathrm and thus: \theta = \arctan where \theta is the angle from horizontal and ''μs'' is the static coefficient of friction between the objects. This formula can also be used to calculate ''μs'' 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 A molecular machine, nanite, or nanomachine is a molecular component that produces quasi-mechanical movements (output) in response to specific stimuli (input). In cellular biology, macromolecular machines frequently perform tasks essential for l ...
. 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 was used to drag a
cobalt Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, p ...
atom, and a
carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...
molecule, across surfaces of copper and
platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Pla ...
.


Limitations of the Coulomb model

The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area; that this
contact area When two objects touch, only a certain portion of their surface areas will be in contact with each other. This area of true contact, most often constitutes only a very small fraction of the apparent or ''nominal'' contact area. In relation to two c ...
is proportional to the normal force (until saturation, which takes place when all area is in atomic contact); and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. 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 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 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 is a type of motor racing in which automobiles or motorcycles compete, usually two at a time, to be first to cross a set finish line. The race follows a short, straight course from a standing start over a measured distance, most ...
tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.


"Negative" coefficient of friction

, a single study has demonstrated the potential for an ''effectively negative coefficient of friction in the low-load regime'', meaning that a decrease in normal force leads to an increase in friction. This contradicts everyday experience in which an increase in normal force leads to an increase in friction. This was reported in the journal ''Nature'' in October 2012 and involved the friction encountered by an atomic force microscope stylus when dragged across a graphene sheet in the presence of graphene-adsorbed oxygen. *


Numerical simulation of the Coulomb model

Despite being a simplified model of friction, the Coulomb model is useful in many
numerical simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
applications such as multibody systems and
granular material A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose ...
. 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 mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite nonlinear effects, such as the so-called
Painlevé paradox In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minist ...
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. These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding, by material expansion due to heat generation during friction (the thermo-elastic instabilities), or by pure dynamic effects of sliding of two elastic materials (the Adams–Martins instabilities). The latter were originally discovered in 1995 by George G. Adams and João Arménio Correia Martins for smooth surfaces and were later found in periodic rough surfaces. In particular, friction-related dynamical instabilities are thought to be responsible for brake squeal and the 'song' of a glass harp, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity. A practically important case is the self-oscillation of the strings of bowed instruments such as the
violin The violin, sometimes known as a '' fiddle'', is a wooden chordophone ( string instrument) in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument ( soprano) in the family in regu ...
,
cello The cello ( ; plural ''celli'' or ''cellos'') or violoncello ( ; ) is a bowed (sometimes plucked and occasionally hit) string instrument of the violin family. Its four strings are usually tuned in perfect fifths: from low to high, C2, G2, ...
,
hurdy-gurdy The hurdy-gurdy is a string instrument that produces sound by a hand-crank-turned, rosined wheel rubbing against the strings. The wheel functions much like a violin bow, and single notes played on the instrument sound similar to those of a vi ...
, erhu, etc. A connection between dry friction and flutter instability in a simple mechanical system has been discovered, watch th
movie
for more details. Frictional instabilities can lead to the formation of new self-organized patterns (or "secondary structures") at the sliding interface, such as in-situ formed tribofilms which are utilized for the reduction of friction and wear in so-called self-lubricating materials.


Fluid friction

Fluid friction occurs between
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
layers that are moving relative to each other. This internal resistance to flow is named ''
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
''. In everyday terms, the viscosity of a fluid is described as its "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. The less viscous the fluid, the greater its ease of deformation or movement. All real fluids (except superfluids) offer some resistance to shearing and therefore are viscous. For teaching and explanatory purposes it is helpful to use the concept of an inviscid fluid or an ideal fluid which offers no resistance to shearing and so is not viscous.


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 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 and rises with the square of the velocity. Skin friction is caused by viscous drag in the
boundary layer In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary cond ...
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 deformation.
Plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
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. The force causing it is called
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
. Elastic deformation in solids is reversible change in the internal molecular structure of an object. 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 known as elastic deformation or elasticity.


Radiation friction

As a consequence of light pressure,
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
in 1909 predicted the existence of "radiation friction" which would oppose the movement of matter. He wrote, "radiation will exert pressure on both sides of the plate. The forces of pressure exerted on the two sides are equal if the plate is at rest. However, if it is in motion, more radiation will be reflected on the surface that is ahead during the motion (front surface) than on the back surface. The backward-acting force of pressure exerted on the front surface is thus larger than the force of pressure acting on the back. Hence, as the resultant of the two forces, there remains a force that counteracts the motion of the plate and that increases with the velocity of the plate. We will call this resultant 'radiation friction' in brief."


Other types of friction


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 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 A motor vehicle, also known as motorized vehicle or automotive vehicle, is a self-propelled land vehicle, commonly wheeled, that does not operate on rails (such as trains or trams) and is used for the transportation of people or cargo. The ...
tires on a
road A road is a linear way for the conveyance of traffic that mostly has an improved surface for use by vehicles (motorized and non-motorized) and pedestrians. Unlike streets, the main function of roads is transportation. There are many types o ...
, a process which generates heat and
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
as by-products.


Braking friction

Any wheel equipped with a
brake A brake is a mechanical device that inhibits motion by absorbing energy from a moving system. It is used for slowing or stopping a moving vehicle, wheel, axle, or to prevent its motion, most often accomplished by means of friction. Backgroun ...
is capable of generating a large retarding force, usually for the purpose of slowing and stopping a vehicle or piece of rotating machinery. Braking friction differs from rolling friction because the coefficient of friction for rolling friction is small whereas the coefficient of friction for braking friction is designed to be large by choice of materials for brake pads.


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 An explosion is a rapid expansion in volume associated with an extreme outward release of energy, usually with the generation of high temperatures and release of high-pressure gases. Supersonic explosions created by high explosives are known ...
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.


Reducing friction


Devices

Devices such as wheels,
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 ...
s,
roller bearing In mechanical engineering, a rolling-element bearing, also known as a rolling bearing, is a bearing which carries a load by placing rolling elements (such as balls or rollers) between two concentric, grooved rings called races. The relative m ...
s, and air cushion or other types of
fluid bearing Fluid bearings are bearings in which the load is supported by a thin layer of rapidly moving pressurized liquid or gas between the bearing surfaces. Since there is no contact between the moving parts, there is no sliding friction, allowing flu ...
s can change sliding friction into a much smaller type of rolling friction. Many
thermoplastic A thermoplastic, or thermosoft plastic, is any plastic polymer material that becomes pliable or moldable at a certain elevated temperature and solidifies upon cooling. Most thermoplastics have a high molecular weight. The polymer chains associate ...
materials such as
nylon Nylon is a generic designation for a family of synthetic polymers composed of polyamides ( repeating units linked by amide links).The polyamides may be aliphatic or semi-aromatic. Nylon is a silk-like thermoplastic, generally made from pet ...
, 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 resistance, very high
molecular weight A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bio ...
grades are usually specified for heavy duty or critical bearings.


Lubricants

A common way to reduce friction is by using a
lubricant A lubricant (sometimes shortened to lube) is a substance that helps to reduce friction between surfaces in mutual contact, which ultimately reduces the heat generated when the surfaces move. It may also have the function of transmitting forces, t ...
, 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 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. Tribology is highly interdisciplinary, drawing on many academic fi ...
. 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 Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
: 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 Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and video data, and is often ...
.


Energy of friction

According to the law of
conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means tha ...
, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into thermal energy. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat which raises the thermal energy of the puck and the ice surface. Since heat quickly dissipates, many early philosophers, including
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
, wrongly concluded that moving objects lose energy without a driving force. When an object is pushed along a surface along a path C, the energy converted to heat is given by a
line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; '' contour integral'' is used as well, ...
, in accordance with the definition of work :E_ = \int_C \mathbf_\mathrm(\mathbf) \cdot d\mathbf\ = \int_C \mu_\mathrm\ \mathbf_\mathrm(\mathbf) \cdot d\mathbf, where * \mathbf_\mathrm is the friction force, * \mathbf_\mathrm is the vector obtained by multiplying the magnitude of the normal force by a unit vector pointing ''against'' the object's motion, * \mu_\mathrm is the coefficient of kinetic friction, which is inside the integral because it may vary from location to location (e.g. if the material changes along the path), * \mathbf is the position of the object. Energy lost to a system as a result of friction is a classic example of thermodynamic irreversibility.


Work of friction

In the reference frame of the interface between two surfaces, static friction does ''no'' 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. 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, 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 is the process of creating a smooth and shiny surface by rubbing it or by applying a chemical treatment, leaving a clean surface with a significant specular reflection (still limited by the index of refraction of the material accordin ...
. The work of friction is used to mix and join materials such as in the process of friction welding. Excessive erosion or wear of mating sliding surfaces occurs when work due to frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces in relative motion (
fretting Fretting refers to wear and sometimes corrosion damage of loaded surfaces in contact while they encounter small oscillatory movements tangential to the surface. Fretting is caused by adhesion of contact surface asperities, which are subsequent ...
) exacerbates wear of frictional forces. As surfaces are worn by work due to friction, fit and
surface finish Surface finish, also known as surface texture or surface topography, is the nature of a surface as defined by the three characteristics of lay, surface roughness, and waviness.. It comprises the small, local deviations of a surface from the p ...
of an object may degrade until it no longer functions properly. For example, bearing seizure or failure may result from excessive wear due to work of friction.


Applications

Friction is an important factor in many
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
disciplines.


Transportation

* Automobile brakes inherently rely on friction, slowing a vehicle by converting its kinetic energy into heat. Incidentally, dispersing this large amount of heat safely is one technical challenge in designing brake systems. Disk brakes rely on friction between a disc and
brake pads Brake pads are a component of disc brakes used in automotive and other applications. Brake pads are composed of steel backing plates with friction material bound to the surface that faces the disc brake rotors. Function Brake pads convert the kin ...
that are squeezed transversely against the rotating disc. In drum brakes, brake shoes or pads are pressed outwards against a rotating cylinder (brake drum) to create friction. Since braking discs can be more efficiently cooled than drums, disc brakes have better stopping performance. * Rail adhesion refers to the grip wheels of a train have on the rails, see Frictional contact mechanics. * Road slipperiness is an important design and safety factor for automobiles **
Split friction Split friction (or μ (mu) - split) is a road condition that occurs 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 soft ...
is a particularly dangerous condition arising due to varying friction on either side of a car. **
Road texture Road surface textures are deviations from a planar and smooth surface, affecting the vehicle/tyre interaction. Pavement texture is divided into: microtexture with wavelengths from 0 mm to , macrotexture with wavelengths from to and megatextu ...
affects the interaction of tires and the driving surface.


Measurement

*A tribometer is an instrument that measures friction on a surface. *A profilograph is a device used to measure pavement surface roughness.


Household usage

*Friction is used to heat and ignite
matchsticks A match is a tool for starting a fire. Typically, matches are made of small wooden sticks or stiff paper. One end is coated with a material that can be ignited by friction generated by striking the match against a suitable surface. Wooden ma ...
(friction between the head of a matchstick and the rubbing surface of the match box). * Sticky pads are used to prevent object from slipping off smooth surfaces by effectively increasing the friction coefficient between the surface and the object.


See also

* Contact dynamics * Contact mechanics * Factor of adhesion *
Friction Acoustics Solid bodies in contact that undergo shear relative motion ( friction) radiate energy. Part of this energy is radiated directly into the surrounding fluid media, and another part radiates throughout the solid bides and the connecting boundary cond ...
*
Frictionless plane The frictionless plane is a concept from the writings of Galileo Galilei. In his 1638 '' 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 e ...
*
Galling Galling is a form of wear caused by adhesion between sliding surfaces. When a material galls, some of it is pulled with the contacting surface, especially if there is a large amount of force compressing the surfaces together. Galling is cau ...
* Non-smooth mechanics * Normal contact stiffness *
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 Below is a simple, heuristic description of stic ...
*
Transient friction loading Transient friction loading is the mechanical stress induced on an object due to transient or vibrational frictional forces. Examples A classic example of transient friction loading is the wooden block sliding over an unlevel, non-planar surface. Du ...
*
Triboelectric effect The triboelectric effect (also known as triboelectric charging) is a type of contact electrification on which certain materials become electrically charged after they are separated from a different material with which they were in contact. Rubb ...
* Unilateral contact * Friction torque


References


External links

*
Coefficients of Friction
– tables of coefficients, plus many links
Physclips: Mechanics with animations and video clips
from the University of New South Wales
Values for Coefficient of Friction
– ''
CRC Handbook of Chemistry and Physics The ''CRC Handbook of Chemistry and Physics'' is a comprehensive one-volume reference resource for science research. First published in 1914, it is currently () in its 103rd edition, published in 2022. It is sometimes nicknamed the "Rubber Bible ...
''
Characteristic Phenomena in Conveyor ChainAtomic-scale Friction Research and Education Synergy Hub (AFRESH)
an Engineering Virtual Organization for the atomic-scale friction community to share, archive, link, and discuss data, knowledge and tools related to atomic-scale friction.
Coefficients of friction of various material pairs in atmosphere and vacuum
{{Authority control Classical mechanics Force Tribology