NDA Physics · Laws of Motion and Forces

Friction

Friction is the contact force that opposes relative sliding between surfaces; its limiting value is f = μN, where μ is the coefficient of friction and N is the normal force.

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Why this matters

A small but reliable subtopic — roughly 3 PYQs across 2023–2024. Two ideas cover it: the limiting-friction formula f = μN, and the ordering static > kinetic > rolling friction. Computations are direct substitutions; the only subtlety is using the correct normal force (which equals the weight only on flat ground).

Concept 1 of 3

Limiting (maximum) friction, f = μN

Intuition

Friction adjusts itself to oppose whatever push you apply — up to a maximum. That maximum, the limiting friction, is proportional to how hard the surfaces are pressed together (the normal force), with the constant of proportionality being the coefficient of friction. Heavier or more strongly pressed surfaces grip harder; smoother surfaces (smaller μ) grip less.

Definition

Limiting (maximum static) friction is $f_{\max} = \mu N$ , where $\mu$ is the coefficient of friction and $N$ is the normal force pressing the surfaces together. On a horizontal surface with no vertical applied force, $N = mg$ , so $f_{\max} = \mu m g$ . Friction is independent of the apparent contact area; it depends only on $\mu$ and $N$ .

Limiting friction

f_{\max} = \mu N

f_maxmaximum (limiting) friction force
μcoefficient of friction (dimensionless)
Nnormal force (= mg on flat ground)

On an incline, weight splits into mg sin θ (along the slope, the driving force) and mg cos θ (into the slope, which sets N). Maximum friction is μN = μ mg cos θ — it depends on the cosine component, not the full weight.

Worked example

A 5 kg block rests on a horizontal floor with coefficient of friction 0.3 (take g = 10 m/s²). What horizontal force is just enough to start it moving?

On flat ground the normal force equals the weight: $N = mg = 5 \times 10 = 50\,\text{N}$ .
Limiting friction: $f_{\max} = \mu N = 0.3 \times 50 = 15\,\text{N}$ .
The block starts to move once the applied force just exceeds 15 N.

Answer:15 N (the applied force must just exceed the limiting friction).

Practice this conceptself-check · 4 quick reps

Try it yourself

A 2 kg block sits on top of a 3 kg block; the coefficient of static friction between them is 0.2 (g = 10 m/s²). The bottom block is pulled so both move together. What is the maximum friction force available on the top block?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
What is the formula for limiting friction?
2.
On flat ground with no vertical push, the normal force equals what?
3.
Block of 4 kg, μ = 0.25, g = 10: limiting friction?
4.
Does friction depend on the apparent area of contact?

From the bank · past-year question

Example 1Laws of Motion and ForcesMODERATE

One block of 2·0 kg mass is placed on top of another block of 3·0 kg mass. The coefficient of static friction between the two blocks is 0·2. The bottom block is pulled with a horizontal force F such that both blocks move together without slipping. Taking acceleration due to gravity as 10 m/s

^2

, the maximum value of the frictional force is :

[Q124 · Apr · 2023]

Use the correct normal force, not always mg

f = μN uses the NORMAL force, which equals mg only on flat ground with no vertical applied force. On an incline N = mg cos θ; for a block on top of another, N is the upper block's weight. Plugging the full weight when the geometry says otherwise is the most common friction error.

Concept 2 of 3

Friction as the only horizontal force — stopping a block

Intuition

When a block slides to a stop on a rough surface, friction is the only horizontal force, so it provides the full deceleration. You can find the friction either from the energy it dissipates over the stopping distance, or from F = ma using the deceleration. Both routes give the same answer.

Definition

For a block decelerating on a rough horizontal surface, friction is the net horizontal force: $f = ma$ . Using kinematics $v^2 = u^2 - 2as$ (final $v = 0$ ) gives the deceleration, or use work-energy: the friction work $f\,s$ equals the lost kinetic energy $\tfrac12 m u^2$ .

Friction from stopping (work-energy form)

f \, s = \tfrac{1}{2} m u^2 \;\Rightarrow\; f = \frac{m u^2}{2s}

ffrictional force
sstopping distance
uinitial speed
mmass of the block

Worked example

A 2 kg block moving at 3 m/s comes to rest on a rough horizontal surface after sliding 3 m. Find the frictional force.

Friction work over the distance equals the kinetic energy lost: $f\,s = \tfrac12 m u^2$ .
$\tfrac12 m u^2 = \tfrac12 \times 2 \times 3^2 = 9\,\text{J}$ .
So $f \times 3 = 9$ , giving $f = 3\,\text{N}$ .

Answer:3 N.

Practice this conceptself-check · 4 quick reps

Try it yourself

A 4 kg block sliding at 4 m/s stops in 2 m on a rough floor. Find the friction force using kinematics and F = ma.

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
A block stops on a rough floor. What is the only horizontal force on it?
2.
2 kg block at 3 m/s stops in 3 m. Friction force?
3.
Friction work over distance s equals what?
4.
1 kg block at 2 m/s stops in 1 m. Friction?

From the bank · past-year question

Example 2Laws of Motion and ForcesEASY

A block of mass 2 kg, moving with the initial speed of 3 m/s comes to rest on a rough horizontal surface after travelling a distance of 3 m. The magnitude of the frictional force is :

[Q132 · Apr · 2024]

Concept 3 of 3

Static, kinetic, and rolling friction

Intuition

Friction comes in three flavours that decrease in strength as motion gets easier. Static friction (before sliding starts) is the strongest — it's why it takes a big shove to get something moving. Kinetic friction (while sliding) is a bit less. Rolling friction (a wheel rolling) is the smallest — which is exactly why wheels and ball bearings are used.

Definition

Three regimes, in decreasing order of strength:

Static friction — acts before sliding begins; self-adjusts up to a maximum $\mu_s N$ . The largest of the three.
Kinetic (sliding) friction — acts during sliding, $\mu_k N$ ; roughly constant and slightly less than the limiting static value.
Rolling friction — acts when a body rolls; the smallest, which is why rolling beats dragging.

Ordering: static > kinetic > rolling.

Type	When it acts	Relative size
Static	Before sliding starts	Largest (up to μ_s N)
Kinetic / sliding	While the body slides	Intermediate (μ_k N)
Rolling	While the body rolls	Smallest NDA 2024 — the correct ordering is Static friction > Kinetic friction > Rolling friction.

Rolling friction is the smallest, which is why wheels and ball bearings reduce resistance. NDA tests the ordering directly.

Practice this conceptself-check · 4 quick reps

Try it yourself

Why is it harder to START pushing a heavy crate than to KEEP it moving once it slides?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Order static, kinetic, and rolling friction from largest to smallest.
2.
Which friction acts before a body starts to slide?
3.
Why do we use wheels and ball bearings?
4.
Is kinetic friction larger or smaller than limiting static friction?

From the bank · past-year question

Example 3Laws of Motion and ForcesEASY

Which one of the following about different frictional forces is correct ?

[Q88 · Apr · 2024]

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Limiting (maximum) friction, f = μN
Limiting friction
$f_{\max} = \mu N$
Friction as the only horizontal force — stopping a block
Friction from stopping (work-energy form)
$f \, s = \tfrac{1}{2} m u^2 \;\Rightarrow\; f = \frac{m u^2}{2s}$

Reference tables (1)

Static, kinetic, and rolling friction3 rows

Type	When it acts	Relative size
Static	Before sliding starts	Largest (up to μ_s N)
Kinetic / sliding	While the body slides	Intermediate (μ_k N)
Rolling	While the body rolls	Smallest NDA 2024 — the correct ordering is Static friction > Kinetic friction > Rolling friction.

Rolling friction is the smallest, which is why wheels and ball bearings reduce resistance. NDA tests the ordering directly.

Watch out for (1)

Use the correct normal force, not always mg
→ Limiting (maximum) friction, f = μN

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