---
title: "Angle of friction; laws of static friction"
subject: "Applied Mechanics"
chapter: 5
key: "semester_1/applied_mechanics:angle-of-friction-laws-static-friction"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/angle-of-friction-laws-static-friction
site: BCT Engineering
---

# Angle of friction; laws of static friction

Applied Mechanics · Chapter 5: Friction

- Asked in: 2070 Chaitra, 4 marks
- Video: [Laws of Friction | Law of Static And Dynamic Friction | Engineering Mechanics](https://www.youtube.com/watch?v=Ssj7rAnzn84) — TRISHAKTI ACADEMY
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/angle-of-friction-laws-static-friction
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-5

## Question

Define the angle of friction and also write the laws of static friction.

## Short answer

Angle of friction φ satisfies tan φ = μ, the angle between the normal reaction and the resultant of normal and limiting friction. Laws of static friction: it opposes motion, is self-adjusting up to μN, independent of area, depends on surface nature; kinetic friction is slightly less than maximum static.

## Answer

#### Angle of friction
The angle of friction φ is the angle between the normal reaction N and the resultant R of the normal reaction and the limiting friction force F_max. At the point of impending motion,
tan φ = F_max / N = μₛ, so φ = tan⁻¹ μₛ.
```text
        N
        ^   /R
        |  /
        | / φ
 -------+/-------> F_max
```
A body on an inclined plane is just on the point of sliding when the angle of the incline equals φ (angle of repose).

#### Laws of static friction
1. The friction force always acts opposite to the direction of the impending motion.
2. Friction is self-adjusting: it equals the applied force until the limit is reached, so F ≤ μₛN.
3. The limiting friction is proportional to the normal reaction: F_max = μₛN.
4. It is independent of the area of contact.
5. It depends on the nature and roughness of the surfaces, which give the value of μₛ.
6. When motion starts, the friction force drops to the kinetic value μₖN (μₖ < μₛ).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The angle of friction is the angle between which two vectors?
   A. Applied force and friction force
   B. Weight and normal reaction
   C. Normal reaction N and the resultant R of N and F_max
   D. Friction force and the horizontal
   Answer: C. phi is measured between N and the resultant R of N and limiting friction. (Key point: Definition of angle of friction)

2. At impending motion, tan phi equals what?
   A. mu_k
   B. mu_s (= F_max / N)
   C. N / F_max
   D. W / N
   Answer: B. tan phi = F_max/N = mu_s, so phi = tan^-1 mu_s. (Key point: Value of tan phi)

3. What does 'friction is self-adjusting' mean?
   A. Friction equals the applied force until the limit F = mu_s N is reached
   B. Friction is always equal to mu_s N
   C. Friction increases with contact area
   D. Friction is constant at any applied force
   Answer: A. Below the limit, friction exactly balances the applied force, so F <= mu_s N. (Key point: Self-adjusting friction)

4. A body on an incline is just about to slide when the incline angle equals what?
   A. Half the angle of friction
   B. 90° minus phi
   C. The angle whose sine is mu_s
   D. The angle of friction phi
   Answer: D. On an incline, tan(theta) = mu_s at the point of sliding, so theta = phi (angle of repose). (Key point: Angle of repose)

## Related in Applied Mechanics

- [Laws of dry friction; overturning and sliding](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alaws-dry-friction-overturning-sliding) — Applied Mechanics, chapter 5
- [Laws of friction; usage in engineering](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alaws-of-friction-engineering-usage) — Applied Mechanics, chapter 5
- [Define limiting friction, angle of friction, coefficients](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alimiting-friction-angle-coefficient-definitions) — Applied Mechanics, chapter 5
- [Limiting friction; why μs > μk](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Alimiting-friction-impending-motion-static-vs-kinetic) — Applied Mechanics, chapter 5

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