AP Physics C: Mechanics · Unit 2: Force and Translational Dynamics · Lesson 2.7

Deep Dive: Kinetic and Static Friction

🔬 Deep Dive
This is your textbook for this topic. Take your time. Read it more than once.
2.7.A.12.7.A.1.i2.7.A.1.ii2.7.A.22.7.A.2.i2.7.A.2.iiConceptMath

Kinetic Friction

Kinetic friction occurs only when two surfaces in contact are already sliding relative to each other. It always acts opposite the direction of that relative sliding motion.

Fk = μₖN
🔑Here's the counterintuitive part: friction force does not depend on the size of the contact area. A brick lying flat has far more surface area touching the ground than the same brick standing on end — but the friction force is identical either way, since normal force (not contact area) is what actually determines it.
Small contact areaLarge contact areaSame mass, same μ, wildly different contact area→ identical friction force

The coefficient of kinetic friction, μₖ, depends only on the material properties of the two surfaces in contact — rubber on concrete has a different μₖ than wood on ice, regardless of the size or shape of either object. Normal force itself is just the perpendicular component of the contact force a surface exerts, always directed away from the surface.

2.7.B.12.7.B.22.7.B.2.iConceptMath

Static Friction: A Force That Adapts

Static friction can occur between two surfaces that are not moving relative to each other. Unlike kinetic friction, static friction isn't a single fixed value — it adopts whatever magnitude and direction is needed to prevent the surfaces from slipping or sliding.

fs ≤ μₛN
⚠️That's an inequality, not an equation you can just plug into. Static friction could be zero (nothing is trying to slide anything), or it could be right at its maximum (about to slip) — or anywhere in between. Solve for whatever value equilibrium actually demands; only assume fs = μₛN if the problem tells you the object is on the verge of slipping.

Slipping and sliding both describe surfaces moving relative to each other — the moment that starts happening, you've left the static regime and kinetic friction takes over.

Try the classic friction-response experiment below: push a stationary block harder and harder, and watch friction match your push exactly — right up until it can't.

A 10 kg block on a horizontal surface. Push harder and harder — friction matches your push exactly, right up until it can't anymore, then drops to the (typically lower) kinetic value and stays there.

Applied force8 N
μₛ (static)0.50
μₖ (kinetic)0.35
fF(applied) →static: f = F(applied)kinetic: f = μₖN (constant)
Max static = 50.0 NKinetic = 35.0 NCurrent friction = 8.0 N

The block is still stationary — static friction is exactly matching your applied force.

2.7.B.2.ii2.7.B.3Math

Maximum Static Friction and the Slipping Point

There's a hard ceiling on how large static friction can get for a given pair of surfaces and normal force:

Fs,max = μₛN

Push (or tilt) past this maximum, and the surfaces start to slide — at which point you switch entirely from static friction's rulebook to kinetic friction's fixed value.

🔑For a given pair of surfaces, μₛ is typically greater than μₖ — it genuinely takes more force to start something sliding than it takes to keep it sliding once it's already moving. This is why a heavy box seems to "break free" with a jolt the instant it starts moving.

This maximum is exactly what the classic "raise the ramp until it slips" experiment measures. Try it yourself below, using the incline block from this unit's header art.

The incline block from this unit's header, on a surface with no other forces besides gravity, normal force, and friction. Slowly raise the angle — find the point where static friction can no longer hold it.

θ (angle)15.0°
μₛ0.40
μₖ0.25
✓ Held — static friction is enough
Gravity's pull down the incline: 12.9 N
Max static friction available: 19.3 N
Critical angle (tan⁻¹ μₛ): 21.8°

This is exactly the classic experiment for measuring μₛ: raise the surface until the object just barely starts to slide, then tan θ(critical) = μₛ.

ExampleGuided Example — Finding μₛ from a Critical Angle

A block on an adjustable incline just barely starts to slide when the incline reaches 22°. Find the coefficient of static friction between the block and the incline.

Step 1Identify the condition at the critical angle
At the exact instant of slipping, static friction is at its maximum: fs = fs,max = μₛN
ExampleWorked Example — Comparing μₛ and μₖ

The same incline and block from above continues to accelerate down the slope once sliding begins, reaching 2.1 m/s² at the same 22° angle. Find μₖ, and confirm it's less than the μₛ found above.

← Back to Lesson 2.7Ready for 2.8? Spring Forces introduces Hooke's law — the next specific force to add to F=ma.