Friction

Q: Why is kinetic friction less than static friction?

When surfaces are at rest, tiny irregularities settle and form microscopic cold welds requiring a larger force to break. Once sliding starts, surfaces do not get time to form fresh welds, so resistance drops. Hence coefficient of kinetic friction is less than coefficient of static friction.

Q: Does friction depend on the area of contact?

For rigid bodies, no. Friction is mu N which depends only on the coefficient and normal reaction. The actual microscopic contact area at asperities is proportional to load, not visible area. This is the Amontons-Coulomb result.

Q: What is the physical significance of the angle of friction?

The angle of friction is the maximum angle the total contact reaction can tilt away from the normal before sliding starts. Applied forces within this angle cannot cause sliding, forming the basis of self-locking mechanisms.

Q: Why do we need friction to walk?

When you push your foot backward against the ground, friction from the ground on your foot acts forward by Newton's Third Law. This forward friction propels you. On a frictionless surface your foot would slip and you could not walk.

Q: Is the angle of repose the same for all surfaces?

No. Since tan of angle of repose equals mu s, it depends on the coefficient of static friction between the two surfaces. Rougher pairs have larger angles of repose; smoother pairs like ice on ice have very small angles.

Q: Why does a car skid on a wet road?

Water forms a thin film between tyre and road, reducing effective friction. Since centripetal force needed for turning must be provided by friction, a smaller mu means smaller maximum safe speed. Exceeding this speed causes skidding.

Q: How does lubrication reduce friction?

Lubricants form a thin layer between surfaces. Direct asperity contact is prevented; instead lubricant layers slide over each other. The internal viscosity of the lubricant is much lower than friction between the original surfaces.

Q: Can friction ever help in causing motion?

Yes. Friction opposes relative motion but can cause absolute motion. When a car accelerates, tyres push the road backward and friction acts forward on the tyres, propelling the car. Walking works the same way through static friction on your foot.

Q: Why is rolling friction so much less than sliding friction?

In rolling, only a small area contacts the surface at any instant and there is no relative sliding at that point. Losses come from small elastic deformations rather than continuously breaking cold welds, making rolling friction much smaller than sliding friction.

PhysicsLaws of MotionFor JEE aspirants

Friction is the contact force that opposes relative motion (or the tendency of relative motion) between two surfaces in contact. It acts along the surfaces, perpendicular to the normal reaction. Friction is classified into static friction (when surfaces are not sliding), kinetic friction (when surfaces are sliding), and rolling friction (when one surface rolls over the other). For JEE and NEET, the essential formulas are limiting static friction $f_{s}^{ma x} = μ_{s} N$ , kinetic friction $f_{k} = μ_{k} N$ , angle of friction $tan λ = μ_{s}$ , and angle of repose $tan θ_{r} = μ_{s}$ .

Key Formulas - Quick Reference

Limiting static friction: $f_{s}^{ma x} = μ_{s} N$
Static friction range: $0 \leq f_{s} \leq μ_{s} N$
Kinetic friction: $f_{k} = μ_{k} N$ (constant, once sliding starts)
Relation: $μ_{k} < μ_{s}$ (kinetic is always less than static)
Angle of friction: $tan λ = μ_{s}$
Angle of repose: $tan θ_{r} = μ_{s}$ (so $θ_{r} = λ$ )
Minimum force to move a body horizontally: $F_{min} = μ_{s} m g$
Acceleration on rough incline (sliding down): $a = g (sin θ - μ_{k} cos θ)$

1. What is Friction?

Frictional force comes into play between two surfaces whenever there is relative motion, or a tendency of relative motion, between them. Friction always opposes the relative motion (or tendency of motion) between the surfaces in contact.

Cause of friction: At a microscopic level, no surface is perfectly smooth. Interlocking of surface irregularities and molecular adhesion at contact points produce a force that resists sliding. Modern theory attributes friction primarily to cold welding of asperities (tiny high points) where the surfaces actually touch.

Types of Friction

Type	When it acts	Nature
Static friction ( $f_{s}$ )	Surfaces in contact but not sliding	Self-adjusting; opposes tendency of motion
Kinetic friction ( $f_{k}$ )	Surfaces sliding over each other	Constant magnitude, opposes relative motion
Rolling friction ( $f_{r}$ )	One surface rolls on another	Much smaller than kinetic; due to deformation at contact

2. Static Friction

Static friction acts between surfaces in contact that are not in relative motion. It opposes the tendency of one surface to slide over the other. Key property: it is self-adjusting.

If you apply a small horizontal force $F$ to a heavy box on the floor and the box does not move, static friction $f_{s} = F$ exactly balances your push. Increase $F$ , and $f_{s}$ increases with it - up to a maximum value called limiting friction:

f_{s}^{ma x} = μ_{s} N

Here $μ_{s}$ is the coefficient of static friction (dimensionless), and $N$ is the normal reaction. The general range of static friction is:

0 \leq f_{s} \leq μ_{s} N

Important: Static friction takes only the value needed to prevent motion. It equals

μ_{s} N

only at the instant sliding is about to begin.

Laws of Static Friction

Static friction is self-adjusting: it adjusts to match the applied force until the limit is reached.
The maximum (limiting) static friction is proportional to the normal reaction: $f_{s}^{ma x} \propto N$ .
It is independent of the apparent area of contact between the surfaces (for rigid bodies).
It depends on the nature of the surfaces in contact (roughness, material).

Figure 1: Friction rises linearly with applied force up to limiting static value μₛN, then drops to kinetic value μₖN as sliding begins.

3. Kinetic Friction

Once the applied force exceeds the limiting static friction, the body begins to slide. Immediately, friction drops to a smaller constant value called kinetic friction:

f_{k} = μ_{k} N

Here $μ_{k}$ is the coefficient of kinetic friction, and it is always slightly less than $μ_{s}$ :

μ_{k} < μ_{s}

Laws of Kinetic Friction

Kinetic friction is independent of the relative speed between the surfaces (for moderate speeds).
It is proportional to the normal reaction: $f_{k} \propto N$ .
It is independent of the apparent area of contact.
It depends on the nature of the two surfaces in contact.

4. Angle of Friction

The angle of friction

λ

is the angle that the resultant of normal reaction and limiting friction makes with the normal reaction (the vertical).

Figure 2: The resultant R of normal reaction N and limiting friction f makes angle λ with the vertical, where tan λ = μs.

From the geometry of the diagram:

tan λ = \frac{f}{N} = \frac{μ _{s} N}{N} = μ_{s}

So the coefficient of static friction equals the tangent of the angle of friction.

5. Angle of Repose

The angle of repose

θ_{r}

is the maximum angle of inclination of a rough surface at which a body placed on it just begins to slide down.

Figure 3: Block on inclined plane at angle θ. At the angle of repose, mg sin θ = μsN, giving tan θr = μs.

Consider a body of mass $m$ on an incline of angle $θ$ . Resolving forces:

Along the incline: $m g sin θ - f = 0 \Rightarrow f = m g sin θ$
Perpendicular to the incline: $N - m g cos θ = 0 \Rightarrow N = m g cos θ$

The body just begins to slide when $f = f_{s}^{ma x} = μ_{s} N$ . At this critical angle $θ = θ_{r}$ :

m g sin θ_{r} = μ_{s} m g cos θ_{r} \Rightarrow tan θ_{r} = μ_{s}

Notice that the angle of repose equals the angle of friction:

θ_{r} = λ

. Both are related to

μ_{s}

by the same equation.

6. Motion on a Rough Inclined Plane

Case 1: Body slides down ( $θ > θ_{r}$ )

Net force along the incline (down the slope):

F_{n e t} = m g sin θ - μ_{k} m g cos θ

a = g (sin θ - μ_{k} cos θ)

Case 2: Body pushed up the incline

Friction acts down the slope (opposing motion). Force required to move up at constant velocity:

F = m g sin θ + μ_{k} m g cos θ = m g (sin θ + μ_{k} cos θ)

Case 3: Minimum force to prevent sliding down ( $θ > θ_{r}$ )

Applied force $F$ acts up the slope; friction also acts up (maximum). Condition:

F_{min} = m g sin θ - μ_{s} m g cos θ

Solved Example 1

A block of weight 2 kg rests on a horizontal surface. Coefficient of static friction is 0.40 and kinetic friction is 0.20. (a) What is the friction force on the block? (b) What is the friction force if a horizontal 5 N force is applied? (c) What is the minimum force required to start the block moving? Take $g = 10 m / s^{2}$ .

Solution:

Normal reaction $N = m g = 2 \cdot 10 = 20 N$ . Limiting static friction $= μ_{s} N = 0.40 \cdot 20 = 8 N$ .

(a) No horizontal force applied and no tendency of motion, so friction = 0.

(b) Applied force 5 N is less than the limiting friction 8 N. Static friction adjusts to equal the applied force: $f_{s} = 5 N$ .

(c) The block starts moving when applied force just exceeds limiting friction: $F_{min} = μ_{s} N = 8 N$ .

Solved Example 2

A block of weight 2 kg is on a horizontal surface. The applied horizontal force can be increased up to 8 N before the block slides. Once moving, a 4 N force keeps it at constant velocity. Find $μ_{s}$ and $μ_{k}$ . ( $g = 10 m / s^{2}$ .)

Solution:

Normal reaction: $N = m g = 20 N$ .

At the point of sliding, applied force equals limiting static friction: $8 = μ_{s} N \Rightarrow μ_{s} = 8/20 = 0.40$ .

At constant velocity, applied force equals kinetic friction: $4 = μ_{k} N \Rightarrow μ_{k} = 4/20 = 0.20$ .

μ_{s} = 0.40, μ_{k} = 0.20

Figure 4: Stacked blocks - friction f₁ acts between A and B (top surface), f₂ between B and ground; μ = 0.25 everywhere.

Solved Example 3

Block A (0.4 kg) rests on top of block B (0.5 kg) on a horizontal surface. A cord attached to A runs horizontally to a fixed wall on the right. The coefficient of sliding friction between all surfaces is 0.25. (a) Find the force $F$ required to drag block B leftward at constant speed. (b) Find the tension in the cord. ( $g = 10 m / s^{2}$ .)

Solution:

Block A analysis: Block A is at rest. Vertically, $N_{1} = m_{1} g = 0.4 \cdot 10 = 4 N$ . Horizontally, the cord tension $T$ balances friction from B on A (which acts leftward, since B moves leftward under A).

$T = μ_{k} N_{1} = 0.25 \cdot 4 = 1 N$

Block B analysis: Block B moves left at constant velocity. Vertically:

$N_{2} = N_{1} + m_{2} g = 4 + 0.5 \cdot 10 = 9 N$

Two frictional forces oppose F: $f_{1}$ from A (reaction to friction A experiences) and $f_{2}$ from the ground.

$f_{1} = μ_{k} N_{1} = 0.25 \cdot 4 = 1 N$

$f_{2} = μ_{k} N_{2} = 0.25 \cdot 9 = 2.25 N$

For constant velocity:

F = f_{1} + f_{2} = 1 + 2.25 = 3.25 N

Tension in cord: $T = 1 N$ .

7. Rolling Friction

When one body rolls over another without slipping, the friction force between them is called rolling friction. It is much smaller than kinetic friction because rolling involves only small elastic deformation at the contact point, not continuous sliding.

f_{r} = μ_{r} N

Typically

μ_{r} << μ_{k} < μ_{s}

. This is why wheels, ball bearings, and rollers are used to reduce friction in machinery and vehicles.

8. Advantages and Disadvantages of Friction

Advantages	Disadvantages
Enables walking and running (foot grips ground)	Causes wear and tear of machine parts
Vehicles need friction for traction, braking, and turning	Reduces efficiency of machines (produces heat)
Nails, screws, and knots hold because of friction	Extra energy needed to overcome it
Writing with a pen or chalk relies on friction	Erosion of surfaces over time

Methods to Reduce Friction

Use lubricants (oil, grease) to reduce direct surface contact.
Polish surfaces to smooth out irregularities.
Convert sliding motion to rolling motion using wheels or ball bearings.
Use streamlined shapes to reduce friction with fluids (drag).

Common Mistakes to Avoid

Watch out

Using $f_{s} = μ_{s} N$ always. This is the maximum value. Static friction is self-adjusting and can be anywhere between 0 and $μ_{s} N$ .
Assuming friction depends on area of contact. It does not (for rigid surfaces). It only depends on the normal reaction and nature of surfaces.
Forgetting that kinetic friction is constant. $f_{k} = μ_{k} N$ regardless of applied force, as long as motion continues.
Using $μ_{s}$ when the body is already moving. Once sliding begins, use $μ_{k}$ , which is smaller.
Wrong direction of friction on incline problems. Friction opposes the tendency of motion, not necessarily the applied force. On an incline where the block is about to slide down, friction acts up the slope - even if no external force is applied.
Confusing angle of friction and angle of repose. They are numerically equal ( $λ = θ_{r}$ ) and both equal $tan^{- 1} μ_{s}$ , but conceptually one is about the resultant reaction and the other about the incline angle.
Ignoring normal force changes on incline. On an incline, $N = m g cos θ$ , not $m g$ .

Frequently Asked Questions

Q1. Why is kinetic friction less than static friction?

When surfaces are at rest, tiny irregularities (asperities) settle into each other and form microscopic "cold welds." Breaking these bonds requires a larger force. Once sliding starts, the surfaces do not get enough time to form fresh welds, so the resistance drops - hence $μ_{k} < μ_{s}$ .

Q2. Does friction depend on the area of contact?

For rigid bodies, no. Friction is $μ N$ , which depends only on the coefficient (surface nature) and the normal reaction. This is because the actual microscopic area of contact (at asperities) is proportional to the load, not the visible area. This is a classical Amontons–Coulomb result.

Q3. What is the physical significance of the angle of friction?

The angle of friction $λ$ tells you the maximum angle by which the total contact reaction can tilt away from the normal to the surface before sliding starts. Any applied force whose line of action makes an angle less than $λ$ with the normal cannot cause sliding, no matter how large it is (for a purely normal-loading direction - this is the basis of self-locking mechanisms).

Q4. Why do we need friction to walk?

When you push your foot backward against the ground, friction from the ground on your foot acts forward (Newton's Third Law reaction). This forward friction is what propels you. On a truly frictionless surface (like slick ice), your foot would just slip backward and you could not walk.

Q5. Is the angle of repose the same for all surfaces?

No. Since $tan θ_{r} = μ_{s}$ , the angle of repose depends on the coefficient of static friction between the two surfaces. Rougher combinations (like rubber on concrete) have larger $μ_{s}$ and hence a larger angle of repose. Smoother pairs (like ice on ice) have very small angles.

Q6. Why does a car skid on a wet road?

Water forms a thin film between the tyre and the road, reducing the effective coefficient of friction. Because the centripetal force required for turning $m v^{2} / r$ must be provided by friction $μ m g$ , a smaller $μ$ means a smaller maximum safe speed. If the driver goes faster than $μg r$ , the required friction exceeds what is available, and the car skids outward.

Q7. How does lubrication reduce friction?

Lubricants (oil, grease, graphite) form a thin layer between the two surfaces. Direct contact between asperities is prevented, and instead the layers of lubricant slide over each other. The internal friction (viscosity) of the lubricant is much lower than the friction between the original surfaces.

Q8. Can friction ever help in causing motion?

Yes. Friction opposes relative motion between surfaces, but it can cause absolute motion of a body. When a car accelerates, the tyres push the road backward (relative motion tendency), and friction on the tyres acts forward, propelling the car. Similarly, when you walk, static friction on your foot is what actually accelerates you.

Q9. Why is rolling friction so much less than sliding friction?

In rolling, only a small area of the wheel is in contact with the surface at any instant, and there is no relative sliding at the point of contact (for pure rolling). The only losses come from small elastic deformations of the wheel and surface, which are much smaller than the energy lost in continuously breaking cold welds during sliding.

Previous year questions on Friction

10 questions from past papers, each with a step-by-step solution.

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1. What is Friction?

Types of Friction

2. Static Friction

Laws of Static Friction

3. Kinetic Friction

Laws of Kinetic Friction

4. Angle of Friction

5. Angle of Repose

6. Motion on a Rough Inclined Plane

Case 1: Body slides down (θ>θr​)

Case 2: Body pushed up the incline

Case 3: Minimum force to prevent sliding down (θ>θr​)

7. Rolling Friction

8. Advantages and Disadvantages of Friction

Methods to Reduce Friction

Common Mistakes to Avoid

Frequently Asked Questions

Q1. Why is kinetic friction less than static friction?

Q2. Does friction depend on the area of contact?

Q3. What is the physical significance of the angle of friction?

Q4. Why do we need friction to walk?

Q5. Is the angle of repose the same for all surfaces?

Q6. Why does a car skid on a wet road?

Q7. How does lubrication reduce friction?

Q8. Can friction ever help in causing motion?

Q9. Why is rolling friction so much less than sliding friction?

Previous year questions on Friction

Ready to master Laws of Motion?

Case 1: Body slides down ( $θ > θ_{r}$ )

Case 3: Minimum force to prevent sliding down ( $θ > θ_{r}$ )