# Friction (science)

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Frictional and other forces acting on a body at rest.

Friction is the force that resists the relative lateral (tangential) motion of solid surfaces, fluid layers, or other materials in contact.

There are various categories of friction, for example:

• Dry friction which resists the relative lateral motion between two solid surfaces in contact. Dry friction is also subdivided into static friction between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces.
• Lubricated friction[1] or fluid friction[2] which resists relative lateral motion of two solid surfaces separated by a layer of gas or liquid. Fluid friction is also used to describe the friction between layers within a fluid that are moving relative to each other.[3][4]

Some important, and somewhat counter-intuitive, facts about sliding friction:

• The amount of friction does not depend on the surface area of contact. It does depend on the normal force between the two bodies, but this has no direct relation with the surface area of contact.
• The amount of friction does not depend directly on the masses of the bodies in contact. There may be an indirect dependence; for instance, the mass determines the gravitational force acting on one body, which determines the normal force needed to balance it, which in turn determines the amount of sliding friction.
• The amount of friction does depend on the nature of the surfaces in contact. This dependence is expressed through coefficients of friction.
• The amount of kinetic friction does not depend on the speed at which the surfaces in contact are moving relative to each other. In this respect, kinetic friction differs from other friction-like phenomena, like viscous force and air resistance.
• In introductory physics courses, the normal and friction forces are typically treated as two distinct and separate forces. Alternatively, they can be viewed simply as two components of a single contact force that is exerted between two objects, namely the components perpendicular to (normal force) and parallel to (friction force) the contact surface. In the case of kinetic friction, this force is always at the same angle ${\displaystyle \tan ^{-1}\mu _{k}}$ with respect to the surface normal. For static friction, the force is always less than or equal to the angle ${\displaystyle \tan ^{-1}\mu _{s}}$ with respect to the surface normal.

## Static friction

The static friction acting between two surfaces in contact satisfies two important rules:

• When static friction acts, it always acts to balance the external applied tangential force, so that there is no net force (and hence, no net acceleration) in the tangential direction. In other words, static friction can never cause relative motion of the surfaces in contact.
• The static friction between two surfaces is bounded from above by the quantity ${\displaystyle \mu _{s}N}$. Here, ${\displaystyle \mu _{s}}$, a quantity called the limiting coefficient of static friction, is a dimensionless quantity dependent on the nature of the surfaces in contact, and ${\displaystyle N}$ denotes the normal force between the two bodies (which, intuitively, describes how hard the two bodies are pressed against each other)

Thus, static friction opposes the tendency of two surfaces at relative rest to accelerate against each other, but cannot exceed a certain amount that depends on the nature of the surfaces, and how hard they are pressed against each other.

Static friction cannot create relative motion

The static friction between two bodies cannot cause them to slip against each other. However, static friction can cause bodies to move. For instance, if you put a tray on a table and push the table, the tray moves along with the table. This is because the static friction between the tray and the table opposes the tendency of the surfaces in contact to slip against each other, hence the tray moves along with the table.

Similarly, it is static friction that allows us to carry a stack of books simply by moving the lowest book in the stack.

Static friction is limited by normal force

Two bodies being in contact is not sufficient for static friction to act between them. It is necessary that the bodies are pressed against each other. For instance, if two blocks are lying side by side on a table, with their surfaces meeting vertically, then there is no static friction between them, so we can move one block without moving the other. On the other hand, if one block is placed on top of the other, there is a normal force between them to balance the gravitational force, and this makes static friction possible.

This is also why the stronger we grip things, the easier it is to prevent them slipping. By increasing the grip on an object, we increase the normal force between our fingers and the objects, which raises the limiting value of the force of static friction.

Static friction depends on the coefficient of static friction

The limiting coefficient of static friction, denoted ${\displaystyle \mu _{s}}$, is a dimensionless constant dependent on both the surfaces in contact. ${\displaystyle \mu _{s}}$ usually takes values of around ${\displaystyle 0.2}$, but it is in principle possible for ${\displaystyle \mu _{s}}$ to be greater than 1.

Also, we typically find that the coefficient of static friction depends on how rough or smooth the surfaces are. Smooth surfaces tend to be more slippery, and hence have lower coefficients of static friction, than rough surfaces.

This also explains the intuitive idea that it is easier to grip a rough surface, than to hold to a slippery surface.

## Kinetic friction

Kinetic friction acts between two surfaces in contact that are sliding against one another. Two facts about kinetic friction:

• Kinetic friction acts in the direction opposite to the relative tangential velocity of the two surfaces.
• The magnitude of kinetic friction is independent of the magnitude of velocity, and is given by ${\displaystyle \mu _{k}N}$. Here, ${\displaystyle \mu _{k}}$ denotes the coefficient of kinetic friction, and ${\displaystyle N}$ denotes the normal force (the extent to which the bodies are pressed against one another).

Kinetic friction opposes direction of velocity, not force

Static friction opposes the direction in which the net external applied tangential force is acting. The direction of kinetic friction is independent of the applied tangential force, and depends only on the tangential velocity.

For instance, if a block is sliding uphill on an incline, then the net external applied force (which comes from gravitational force) as well as the kinetic friction force are in the same direction.

Magnitude of kinetic friction is independent of velocity

This is somewhat counter-intuitive, and in fact does not hold for very large velocities. However, it is a reasonable approximation for low velocities. It is also highly unlike viscous force and air resistance, which have a strong dependence on velocity.

Comparison of static and kinetic friction coefficients

The coefficients of static and kinetic friction for a pair of surfaces are often very close, with the kinetic friction usually somewhat less than the static friction.

## Physical situations related to friction

Motion on an incline

Consider a block on an inclined plane, where the inclined plane makes an angle ${\displaystyle \theta }$ with the horizontal. Suppose ${\displaystyle \mu _{s}}$ and ${\displaystyle \mu _{k}}$ are the coefficients of static and kinetic friction between the surfaces of the block and the inclined plane. An application of the laws of motion and the above outlined laws on static friction yield:

• If ${\displaystyle \tan \theta <\mu _{k}}$, the block remains at rest on the incline. ${\displaystyle \tan }$ denotes the trigonometric tangent function. Moreover, even if it is pushed into motion, it will come to rest after going down some length of the inclined plane.
• If ${\displaystyle \mu _{k}<\tan \theta <\mu _{s}}$, the block remains at rest if it is initially at rest. However, if it is pushed into motion, it keeps accelerating downwards, and does not stop.
• If ${\displaystyle \tan \theta =\mu _{s}}$, the surface just begins to slip. Once the surface starts slipping, it will keep slipping.

The angle ${\displaystyle \tan ^{-1}(\mu _{s})}$ is sometimes termed the angle of repose for the pair of surfaces.

Toppling

Rolling

When a ball rolls on the floor, there is no relative motion of the surfaces of contact. Thus, the nature of friction operating is static friction, and not kinetic friction. In fact, static friction is what makes rolling possible. If there is no friction between the ball and the floor, the ball will just slide along the floor.

## References

1. Andy Ruina and Rudra Pratap (2002). Introduction to Statics and Dynamics. Oxford University Press, page 713.  Not yet released. A preprint in PDF format is available online at Introduction to Statics and Dynamics
2. Russell C. Hibbeler (2006). Engineering Mechanics, 11th Edition. Prentice Hall. ISBN 0-13-221509-8.
3. Ferdinand Beer and E. Russel Johnston, Jr. (1996). Vector Mechanics for Engineers, 6th Edition. McGraw-Hill. ISBN 0-07-005367-7.
4. J.L. Meriam and L.G. Kraige (2002). Engineering Mechanics: Dynamics, 5th Edition. John Wiley & Sons. ISBN 0-471-40645-7.