Friction

Friction as a force opposing motion, with magnitude up to a maximum F ≤ μR (and F = μR at the point of slipping) — on rough horizontal surfaces and slopes, the angle of friction tanα = μ, and F = ma with friction included.

Mechanics · Forces & Newton's laws

Friction

Why it works

Real surfaces are rough: they resist sliding with a friction force. Friction is not a fixed amount — it is exactly as big as it needs to be to prevent motion, *up to a limit*. That limit is proportional to how hard the surfaces are pressed together (the normal reaction

R

F \le \mu R,

where

\mu

is the coefficient of friction between the surfaces. While the body is stationary, friction takes whatever value balances the other forces. When it is on the point of slipping (limiting equilibrium) or already moving, friction is at its maximum:

F = \mu R.

Friction always acts to oppose the motion (or the direction the body is trying to move).On a rough horizontal surface,

R = mg

, so the body won't move until the applied force exceeds the maximum friction

\mu mg

. Once moving, friction is

\mu mg

and you apply

F = ma

to the net force.

On a rough slope, friction acts along the slope, opposing the tendency to slide. The normal reaction is

R = mg\cos\alpha

, so the limiting friction is

\mu mg\cos\alpha

. A body on the slope slides down only if the pull down the slope beats the most friction can hold:

mg\sin\alpha > \mu mg\cos\alpha \;\Rightarrow\; \tan\alpha > \mu.

At the very point of sliding,

\tan\alpha = \mu

— this special angle is the angle of friction.

A warning that creates the classic "two answers" questions: friction can point either way along a slope. A force holding a body in limiting equilibrium might be stopping it sliding down (friction acts up) or about to drag it up (friction acts down) — two different cases, giving two possible answers.