Friction is the force that resists sliding — the reason a pushed box eventually stops and the reason you can walk without slipping. It comes in two flavours: static friction, which holds a stationary object in place, and dynamic friction, which drags on an object already moving. Each has its own equation, and knowing when to use which is the whole game.
📘 What you need to know
Friction opposes motion (or attempted motion) and acts parallel to the surfaces in contact
It arises from tiny imperfections in surfaces rubbing against each other, and produces heat
Static friction acts on a stationary object and can take any value up to a maximum
Dynamic friction acts on a moving object and stays roughly constant
The maximum static friction is larger than the dynamic friction — it’s harder to start something moving than to keep it moving
Where friction comes from
Friction is a force that opposes the motion of an object. It can stop a stationary object from starting to move, and it slows a moving object down. On a microscopic scale, no surface is truly smooth — even polished metal is covered in tiny bumps. When two surfaces touch, these imperfections catch and drag on each other, and that resistance is friction.
Whenever friction does its work, energy is transferred by heating. The rubbing raises the temperature of the objects and their surroundings — which is why your hands warm up when you rub them together, and why brakes get hot. Fluid resistance (drag) is the same idea for an object moving through a liquid or gas, colliding with the fluid’s particles.
Static and dynamic friction
There are two kinds of surface friction to keep straight:
Static friction object stationary
Dynamic friction object moving
Static friction acts when an object is stationary. Cleverly, it matches whatever push or pull you apply — push a heavy crate gently and it doesn’t move, because static friction rises to cancel your push exactly. But it can only rise so far. Once your push exceeds its maximum value, the crate breaks free and starts to slide.
At that moment, friction switches to dynamic friction, which acts on the moving object. For a steady sliding situation, dynamic friction is roughly constant. Crucially, the maximum static friction is larger than the dynamic friction — that’s why a stuck object suddenly lurches once it finally gives, and why it takes more effort to get something moving than to keep it going.
While stationary, friction rises to match your pull (green). At the peak — the maximum static friction — the object breaks free, and friction settles to a lower constant value once it’s moving (blue).
The friction equations
Both kinds of friction depend on the normal reaction forceFN pressing the surfaces together — harder contact means more friction. Each has its own equation.
Static frictionFf ≤ μsFN
The ≤ sign matters: static friction takes whatever value is needed to hold the object still, up to a maximum of μsFN. Here μs is the coefficient of static friction — a number between 0 and 1 that measures how “grippy” the two surfaces are. A larger μs means it’s harder to get them sliding.
Dynamic frictionFf = μdFN
Once the object is moving, dynamic friction has a definite value, μdFN, where μd is the coefficient of dynamic friction. For a given pair of surfaces, μd is smaller than μs — so once you’ve overcome static friction, keeping the object moving is easier.
The single most useful fact here: static friction is a range, dynamic friction is a value. That’s why static friction uses ≤ and dynamic uses =. When a question asks “will it move?”, compare the applied force to the maximum static friction μsFN. When it says “it’s sliding at constant speed,” use the dynamic equation with =.
WE 1
A crate sits on a floor where the normal reaction force is 120 N and the coefficient of static friction is 0.45. A worker pushes the crate horizontally with a force of 40 N. Does the crate move?
Step 1 — find the maximum static frictionFf(max) = μsFN = 0.45 × 120 = 54 NStep 2 — compare with the push
push = 40 N, which is less than 54 N
no — the crate stays stillStatic friction simply rises to match the 40 N push, holding the crate in place. It only moves once the push exceeds 54 N.
Friction on a slope
The classic exam problem is a block resting on an incline. The block’s weight pulls straight down, but on a slope it’s easier to split that weight into two components: one along the slope (trying to slide the block down) and one perpendicular to it (pressing the block into the surface). For a block on a slope at angle θ:
Weight components on a slope
along slope: Fg sinθ into slope: Fg cosθ
On a slope, resolve the weight into a component down the slope (Fg sinθ) and one into the slope (Fg cosθ). The normal reaction equals the into-slope component; friction acts up the slope, opposing the slide.
🛠️ Friction on an incline
Find the weight:Fg = mg.
Resolve it: the down-slope component is Fg sinθ, the into-slope component is Fg cosθ.
Friction balances the slide: for a stationary block, Ff = Fg sinθ.
Normal force equals the into-slope part:FN = Fg cosθ.
Apply the friction equation to find the coefficient: μs ≥ Ff ÷ FN.
WE 2
A 6.0 kg block sits stationary on a slope inclined at 25° to the horizontal. Determine the minimum possible value of the coefficient of static friction. Take g = 9.81 m s−2.
Step 1 — find the weightFg = mg = 6.0 × 9.81 = 58.9 NStep 2 — resolve into slope components
along slope: Ff = 58.9 × sin25° = 24.9 N
into slope: FN = 58.9 × cos25° = 53.3 NStep 3 — apply Ff ≤ μsFNμs ≥ Ff ÷ FN = 24.9 ÷ 53.3μs ≥ 0.47The coefficient must be at least 0.47 to hold the block still — and notice μs ≥ tan25°, since the mass cancels out.
💡 Top tips
Static uses ≤, dynamic uses =. Static friction is a range up to a maximum; dynamic friction is a fixed value.
“Will it move?” → compare the applied force to the maximum static friction μsFN.
On a slope, FN = Fg cosθ, not the full weight — only the perpendicular part presses into the surface.
The mass often cancels in incline problems, leaving μ = tanθ at the point of slipping.
Coefficients have no units — they’re ratios of two forces.
Quick recap: friction opposes motion and comes from surface imperfections rubbing together. Static friction (Ff ≤ μsFN) holds a still object and matches the applied force up to a maximum; dynamic friction (Ff = μdFN) drags on a moving object at a constant value. Max static friction beats dynamic, and on a slope the normal force is Fg cosθ.
⚠ Common mistakes
Using = for static friction — it’s an inequality (≤) up to a maximum, not a fixed value
Taking FN as the full weight on a slope — it’s only the perpendicular component, Fg cosθ
Swapping sin and cos when resolving — the down-slope part uses sinθ, the into-slope part uses cosθ
Giving the friction coefficient a unit — it’s a dimensionless ratio
Assuming friction always equals μsFN — that’s only its maximum, reached at the point of slipping
You’ve now met friction between solid surfaces. When an object moves through a fluid, the same resistive idea applies but the maths is different — the drag depends on speed, size and the fluid’s thickness. That’s next: Hooke’s Law takes a brief detour into stretchy materials first, then we return to fluid resistance with Stokes’ Law.
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