Friction

What is friction?

Friction is a force that opposes relative motion between objects that touch.^[1] It acts parallel to the surfaces in contact, always in the direction that opposes the motion, or the attempted motion.^[1]

That last part matters: friction acts even when nothing is sliding yet. Rest your hand on a table without pushing sideways and the friction is zero; push a little harder and the friction grows with your push, until you push hard enough that your hand slips.^[9]

Friction is a common force, yet its behaviour is complex and still not completely understood.^{[1, 2]} Much of what we understand about friction still rests heavily on observation.^[2]

Two kinds: static and kinetic

Physicists split the friction between dry surfaces into two types.^[9]

• Static friction acts between objects that are not moving relative to each other.^[1] It is a responsive force: it grows to match whatever push you apply, up to a maximum limit.^[1] Push harder than that maximum and the object starts to slip.^[9]
• Kinetic friction acts once the surfaces are sliding, and it is smaller than the static friction needed to get them going.^[1]

Static friction is usually greater than kinetic friction.^[1] You can feel this yourself: once a heavy crate starts to slide, it is easier to keep it moving than it was to get it started.^{[1, 2]} One explanation is that a moving object has fewer points of contact, with fewer molecules sticking the surfaces together, so less force is needed to keep it moving.^{[1, 2]}

Static friction is also what lets things move together. A crate on the bed of a truck speeds up with the truck because static friction pushes it forward, as long as it doesn’t slip.^[1] If the truck accelerates too hard, static friction reaches its limit and the crate slides backward relative to the truck bed.^[1]

How strong is friction?

Physicists describe how strongly two materials grip each other with a number called the coefficient of friction, written μ (the Greek letter mu). There’s one value for static friction (μ_s) and one for kinetic friction (μ_k). The coefficient has no units, and its value is usually between 0 and 1.0, depending on the two surfaces in contact.^[1] Here are typical values from the OpenStax University Physics textbook:^[1]

Surfaces	Static μs	Kinetic μk
Rubber on dry concrete	1.0	0.7
Rubber on wet concrete	0.5–0.7	0.3–0.5
Shoes on wood	0.9	0.7
Steel on steel (dry)	0.6	0.3
Wood on wood	0.5	0.3
Waxed wood on wet snow	0.14	0.1
Shoes on ice	0.1	0.05
Ice on ice	0.1	0.03
Steel on steel (oiled)	0.05	0.03
Steel on ice	0.04	0.02
Teflon on steel	0.04	0.04
Bone lubricated by synovial fluid	0.016	0.015

Treat these numbers as rough guides. The textbooks give them to only one or two digits, a sign that the friction equations are only an approximate description of friction.^{[1, 2]} Different books give it differently: the OpenStax College Physics textbook lists rubber on wet concrete as a single 0.7 (static) and 0.5 (kinetic), at the top of the ranges above.^[2]

Materials matter because part of friction comes from molecules of the two surfaces sticking to each other.^[1] That is why, for example, rubber-soled shoes slip less than leather-soled ones.^[1]

The math (optional)

The size of friction depends on the coefficient and on the normal force N: the force perpendicular to the surfaces.^[1]

• Static friction matches the applied force until it reaches its maximum value, f_s(max) = μ_sN.^{[1, 5]}
• Kinetic friction is roughly constant while sliding: f_k = μ_kN.^[6]

Worked example (an illustration). Take a 20 kg wooden crate on a level wooden floor, and treat the normal force as its weight: 20 kg × 9.8 m/s² ≈ 196 newtons (N). With μ_s = 0.5 for wood on wood, you must push harder than 0.5 × 196 ≈ 98 N to start it moving.^[1] Once it slides, μ_k = 0.3 for wood on wood, so about 0.3 × 196 ≈ 59 N keeps it going at a steady speed.^[1] Push with 50 N before it moves and static friction is exactly 50 N; it only “runs out” at the maximum.^[1]

These are rules of thumb, not laws of nature. The friction formulas are empirical: they were found by experiment and are very useful in practice, but they do not have the status of general principles such as Newton’s second law.^[1] They are not even good approximations for lubricated surfaces or for surfaces sliding past each other at high speeds.^[1]

Friction on a slope

On a slope, the normal force is smaller than the object’s full weight: it equals only the part of the weight that pushes straight into the slope.^[1] So the steeper the slope, the less the surfaces are pressed together.

A slope is also a simple way to measure friction. An object slides down a slope at a constant speed when the forces on it balance, and that fact can be used to measure the coefficient of kinetic friction between two materials.^[1] Because the static coefficient is larger than the kinetic one, the object won’t start sliding until the slope is steeper than the angle that keeps it sliding steadily.^[1]

Friction can also slow things down on a slope. For a snowboarder sliding downhill, if the slope is gentle enough or the kinetic coefficient is large enough, the snowboarder slows down.^[1]

Friction keeps cars on the road

To travel around a curve, a car needs a force pulling it toward the centre of the curve, which physicists call a centripetal force.^[5] On a flat, unbanked curve, friction is the only sideways force on the car, so friction is the centripetal force.^[5]

Tyres that roll without slipping are held by static friction, not kinetic friction, and the most they can give is μ_sN.^[5] So a curve needs a minimum coefficient of friction, or the car will follow a wider curve and leave the road.^[5] Friction plays the same role for roller skates on a rink floor.^[5]

Why does friction happen?

Real surfaces are rough at the micro- and nanoscale.^[10] When two rough surfaces touch, only their high spots meet, so the actual contact area is a tiny fraction of the area it looks like.^[1]

Two things then resist sliding:

1. Interlocking bumps. To get an object moving, you must lift it until it skips along on the tips of the bumps, break the tips off, or both.^[2]
2. Stickiness between molecules. Part of friction comes from adhesive forces between the molecules of the two surfaces.^[1]

Press the surfaces together harder and the real contact area grows, and friction is proportional to that area.^{[1, 10]}

Where does the energy go? When surfaces rub, surface atoms stick and make the atomic lattices vibrate; these vibrations are essentially sound waves, and their energy is turned into heat, which is why rubbing makes things warm.^[1] Chemical reactions linked to wear can also happen between atoms on the rubbing surfaces.^[1]

Two surprising rules

1. The area of contact doesn’t matter (in the simple rules). Two blocks of the same mass but different contact areas need the same force to slide at a constant speed.^[9] The formulas depend on the normal force and the materials, not on the area in contact, a somewhat counterintuitive result.^[1] The microscopic picture above fits this: friction follows the true contact area, which is tiny and grows with the load.^{[1, 10]}
2. Speed barely matters (at low speeds). At small but nonzero speeds, friction is nearly independent of speed.^[1] At high sliding speeds, though, the simple formulas stop being accurate.^[1]

Sticking and slipping

Because the static coefficient is slightly larger than the kinetic one, a surface can catch, slip, catch again and slip again.^[9] This catching and slipping explains the behaviour of chalk on a blackboard, fingernails on glass, and a violin bow on a string.^[9]

Friction and drag

Air and water also resist motion. Drag is sometimes described as “aerodynamic friction”, and one source of an aircraft’s drag is skin friction between air molecules and the aircraft’s surface.^[4] A smooth, waxed surface produces less skin friction than a roughened one.^[4]

But fluid resistance doesn’t follow the same simple rules as sliding friction. For a body sliding across a surface, the friction is roughly constant at μ_kN, while the resistance of a liquid or gas does not behave so simply.^[6] Drag depends on the object’s speed through the fluid.^[6] For large objects such as cyclists, cars and baseballs that aren’t moving too slowly, drag is proportional to the square of the speed.^[6]

Fighting friction: lubrication

Oil a concrete floor and a crate becomes easier both to start and to keep moving.^[2] Lubricating a floor makes both the static and kinetic coefficients considerably smaller.^[1]

Fluid film lubrication is the most desirable kind, because in normal operation the film is thick enough to keep the two load-carrying surfaces completely apart.^[8] Friction is then at a practical minimum, coming only from shearing the liquid film, and there is essentially no wear because the solids hardly touch.^[8] Coefficients of friction on the order of 0.003 or less are reported for hydrodynamic lubrication, one way of forming such a film.^[8]

The film doesn’t always hold. Starting, stopping, misalignment, heavy loads and other service conditions can squeeze the film out, or let the surface bumps break through it, pressing the solids into contact.^[8] When a full film can’t form, some friction and wear usually happen, and very high coefficients of friction can be reached.^[8]

Your body uses lubrication too. Joints are lined with smooth cartilage and produce synovial fluid, which reduces friction and wear.^[1] Saliva helps you swallow, and slippery mucus lies between organs in the body.^{[1, 2]} Artificial hip and knee joints can be made of metals (stainless steel or titanium) or plastic (polyethylene), which also have very small coefficients of friction.^[2]

Tribology: why friction costs so much

The science of friction has its own name. Tribology is the science and technology of interacting surfaces in relative motion, including friction, adhesion, lubrication and wear.^{[10, 8]}

Friction and wear are major causes of machines breaking down and of wasted energy.^[10]

A global study, available through the US Department of Energy, estimates that friction consumes roughly one-fifth of all the energy used worldwide.^[7] The same study says that one-third of all the energy used in transport goes to overcoming friction.^[7] It estimates that new materials, lubricants and design changes could cut losses from friction and wear by 18–40%, saving up to 8.7% of total global energy use and 1.4% of gross national product.^[7]

Friction at the smallest scales

Scientists have made great strides in explaining friction at the atomic scale over the past several decades.^[1] But the rules that work for everyday machines often fail at the nanoscale.^[10] In a NIST calculation for perfectly smooth steel surfaces, once a steel cube is shrunk to 10 μm (a hundredth of a millimetre), friction forces far exceed gravitational forces.^[10] In atomic-scale probe experiments, the shear stress related to the force needed to drag the tip varies by more than a factor of 10¹² and is difficult to predict theoretically.^[1]

According to the OpenStax textbook, this research could lead to nearly friction-free environments that save hundreds of billions of dollars in energy now turned into heat.^[1]

Common misconceptions

• “Smoother always means less friction.” Not quite. Much of friction comes from attraction between molecules, so even perfectly smooth surfaces are not friction-free.^[1] Perfectly smooth, clean surfaces of similar materials would stick together, forming a bond called a cold weld.^[1]
• “Static friction is always μ_sN.” No: μ_sN is only the maximum, and below it static friction simply matches the applied force.^[1]
• “Each pair of materials has one true coefficient.” A NIST paper points out that the everyday coefficient of friction is not an intrinsic property of an interface, because it depends on surface geometry, such as roughness, and on wear.^[10]
• “Friction is always bad.” Friction opposes motion, but it also lets us move, as anyone who has tried to walk on ice knows.^[1] Leonardo da Vinci already saw friction as sometimes useful and even essential, while also limiting how efficient machines can be.^[3]
• “Friction only happens between solids.” Air also resists motion, and one source of an aircraft’s drag is skin friction between air molecules and its surface.^[4]

A short history

Leonardo da Vinci’s first statement of the laws of friction is in a tiny notebook, 92 mm × 63 mm, dating from 1493 and now held at the Victoria and Albert Museum in London, as Professor Hutchings found in research reported by the University of Cambridge.^[3] Leonardo knew that friction between sliding surfaces is proportional to the load pressing them together, and that it doesn’t depend on the apparent area of contact.^[3] Rough drawings under his notes show rows of blocks pulled by a weight hanging over a pulley, the same kind of experiment students might do today.^[3]

He recorded measurements of kinetic friction over a twenty-year period, from 1493–4 to about 1515.^[9] He also grasped that the resistance to a wheel turning comes from friction at its axle bearing, and calculated its effect.^[3] He appreciated that friction depends on the nature of the surfaces and on how well they are lubricated.^[3]

Yet Leonardo’s work had no influence on the subject over the following centuries, and it was unknown to Guillaume Amontons.^[3] Amontons, a French scientist, rediscovered the laws and published them in 1699, and today they are usually credited to him.^{[9, 3]} Charles Augustin Coulomb discovered a third property: kinetic friction does not depend on the speed of sliding, at ordinary speeds.^[9]

The researchers Bowden and Tabor found that, contrary to macroscopic observations, friction is proportional to the true area of contact.^[10] Leonardo’s systematic study is widely seen as the root of the modern science of tribology.^[3]

Try it yourself

• Start vs. keep going. Rest your hand on a table, then push sideways harder and harder until it slips; static friction grows with your push until that moment.^[9]
• Measure a coefficient. Put a coin on a book and slowly tilt the book until the coin slides down at a steady speed.^[1] Notice that the coin only starts to slide at a steeper angle than the one that keeps it sliding, because μ_s is larger than μ_k.^[1]
• Does area matter? Tie a string to a rectangular box and pull it along a table, first lying flat, then standing on its narrow side, and compare how hard you have to pull.
• Change the materials. Try the same book on a tiled floor, a carpet and a sheet of paper, and feel the grip change.
• Simulate it. Try the free PhET Friction simulation listed in the resources below.

Going further

Read Drag for how air and water resist motion, and Newton’s Laws of Motion for the rules that friction plugs into. The free PhET simulations and the OpenStax University Physics textbook listed below let you explore further.