Friction is the force that opposes sliding between surfaces — it can hold a stationary object in place or slow a moving one down. There are two kinds to know: static friction (before it moves) and dynamic friction (once it’s sliding), each linked to the normal force by a coefficient.
📘 What you need to know
Friction opposes motion: it can stop an object starting to move, or slow one that is moving.
Friction comes from the roughness of surfaces in contact; the work done against it is transferred to thermal energy (heating).
Static friction acts on a stationary object and grows to match any push, up to a maximum: Ff ≤ μsFN.
Dynamic friction acts on a sliding object and is roughly constant: Ff = μdFN.
Maximum static friction is larger than dynamic friction (μs > μd); both depend on the normal force FN.
Where friction comes from
Friction acts parallel to the surface, in the direction that opposes (or would oppose) sliding. At the microscopic level, no surface is perfectly smooth — tiny bumps and imperfections on the two surfaces catch on each other. Pulling them past one another takes energy, which is why friction heats things up.
Zoom in and the surfaces are jagged — their bumps catch on each other, which is the source of friction (and the heat it produces).
Static vs dynamic friction
There are two types of surface friction:
Static friction acts when the object is stationary. It doesn’t have a fixed value — it grows to exactly match whatever push or pull is applied, holding the object still, right up to a maximum.
Dynamic friction acts once the object is sliding. For a given situation it has a single, roughly constant value.
Push gently and static friction pushes back just as hard, so nothing moves. Push harder and it keeps matching you — until you reach the maximum it can provide. Past that point the object breaks free and slides, and the friction drops to the (smaller) dynamic value.
Static friction grows to match the push up to its maximum (μsFN). Once the object slips, friction drops to the constant dynamic value (μdFN).
The friction equations
Both kinds of friction depend on the normal force pressing the surfaces together, scaled by a coefficient of friction.
Static friction (stationary)Ff ≤ μsFN
Dynamic friction (sliding)Ff = μdFN
Where μs is the coefficient of static friction and μd the coefficient of dynamic friction. The coefficient is just the ratio of the friction force to the normal force — a number between 0 and 1 — and the larger it is, the harder the surfaces are to slide past one another. Note the static equation uses ≤: static friction only reaches μsFN at the instant the object is about to move.
Quick reference: static friction adjusts up to a maximum (≤ μsFN); dynamic friction is fixed (= μdFN); μs > μd; bigger normal force → more friction.
Worked examples
WE 1
A block resting on a slope
An 8.0 kg block sits, stationary, on a slope at 20° to the horizontal. Friction is what stops it sliding down. Find the minimum coefficient of static friction. (Take g = 9.81 m s⁻².)
Weight: Fg = mg= 8.0 × 9.81 = 78.5 NFriction balances the down-slope part: Ff = Fg sin θ= 78.5 × sin 20° = 26.8 NNormal force: FN = Fg cos θ= 78.5 × cos 20° = 73.7 NThen μs ≥ Ff / FN= 26.8 ÷ 73.7μs ≥ 0.36
WE 2
Friction on a sliding box
A 4.0 kg box slides across a level floor where the coefficient of dynamic friction is 0.30. Find the frictional force on it. (Take g = 9.81 m s⁻².)
On the level, FN = weight = mgFN = 4.0 × 9.81 = 39.2 NDynamic friction: Ff = μd FN= 0.30 × 39.2Ff ≈ 11.8 N
💡 Top tips
Find the normal force first. On a slope it’s Fg cos θ, not just the weight.
Static uses ≤, dynamic uses =. Static friction is “up to” a maximum; dynamic friction has one value.
Friction is parallel to the surface, pointing against the (attempted) motion.
It takes more to start than to keep going — μs > μd, which is why something “jerks” free then slides easily.
Coefficients have no units — they’re a ratio of two forces.
⚠ Common mistakes
Using the weight as the normal force on a slope. Resolve first: FN = Fg cos θ.
Treating static friction as a fixed number. It adjusts to match the push until it hits its maximum.
Assuming friction depends on the contact area. At this level it depends on the normal force and the coefficient, not the area.
Forgetting to convert the angle — make sure your calculator is in degrees when using sin θ and cos θ here.
The “minimum” in WE 1 matters: the block only needs enough friction to balance the down-slope pull. Any coefficient of 0.36 or more keeps it still — that’s why static friction uses ≤. Up next: Hooke’s Law, the force from a stretched or compressed spring.
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