Friction

Friction is the part of the contact force that lies parallel to the surfaces; between the surfaces it opposes relative motion, or impending relative motion.

Static friction is self-adjusting: it takes whatever value, up to a maximum, is needed to prevent sliding, f_s ≤ μ_s N.

Its limiting value (f_s)max = μ_s N depends on the nature of the surfaces but not on the area of contact.

If the applied force is less than the limiting value, static friction equals the applied force and the body stays at rest; it is not automatically μ_s N.

Once sliding begins, kinetic friction acts: f_k = μ_k N, roughly independent of speed and area of contact. Usually μ_k < μ_s.

Friction on a body can act along its direction of motion: the friction on a box on the floor of an accelerating truck points forward and is what accelerates the box.

Rolling friction is much smaller than sliding friction, which is why wheels, ball bearings and lubricants are used to reduce energy loss.

Friction is not purely a nuisance; walking, driving and braking all depend on it.