Maximum Static Friction (f = μₛN)

Static friction is the only force in introductory mechanics that is written with an inequality: f ≤ μₛN. It supplies exactly whatever is needed to prevent sliding, up to a ceiling of μₛN, and this formula computes that ceiling. Press a 500 N normal load onto a surface with μₛ = 0.6 and you can push with anything up to 300 N and nothing moves; at 301 N the object breaks free and the weaker kinetic friction takes over.

That inequality is the single biggest trap: plugging μₛN in as "the friction force" on a stationary object is wrong unless the object is on the verge of slipping. The distinction pays real dividends — a car's tyres grip through static friction as long as they roll, which is why ABS pumps the brakes to keep them from locking into a lower-μₖ skid, and why a driven wheel spinning on ice suddenly has far less traction than one that is merely rolling.