---
title: "Define limiting friction, angle of friction, coefficients"
subject: "Applied Mechanics"
chapter: 5
key: "semester_1/applied_mechanics:limiting-friction-angle-coefficient-definitions"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/limiting-friction-angle-coefficient-definitions
site: BCT Engineering
---

# Define limiting friction, angle of friction, coefficients

Applied Mechanics · Chapter 5: Friction

- Asked in: 2074 Chaitra, 4 marks
- Video: [1. Friction | Limiting Friction | Angle of Friction | Complete Concept](https://www.youtube.com/watch?v=8x59va9CaPI) — MKS TUTORIALS by Manoj Sir
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/limiting-friction-angle-coefficient-definitions
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-5

## Question

Define limiting friction, angle of friction and coefficient of the static and dynamic friction.

## Short answer

Limiting friction is max static friction F_max = μsN. Angle of friction φ = tan⁻¹(μs). Static coefficient μs = F_max/N; kinetic coefficient μk = F_k/N, μk < μs.

## Answer

#### Limiting friction
The maximum value of the static friction force that can be developed between two surfaces in contact, just when sliding is about to begin (impending motion). F_max = μₛ N, where N is the normal reaction. If the applied force exceeds it, motion starts.

#### Angle of friction (φ)
The angle between the normal reaction N and the resultant R of N and the limiting friction force F_max.
tan φ = F_max / N = μₛ, so φ = tan⁻¹ μₛ.

```text
        N
        ^   /R
        |  /
        | / φ
 -------+/--------> F_max
```

#### Coefficient of static friction (μₛ)
The ratio of the limiting friction force to the normal reaction when the body is just about to slide: μₛ = F_max / N. It depends on the materials and the surface condition, not on the area of contact.

#### Coefficient of dynamic (kinetic) friction (μₖ)
The ratio of the friction force to the normal reaction when the body is sliding: μₖ = F_k / N. It is slightly less than μₛ, and nearly independent of speed at low speeds.

| | Static | Dynamic |
|---|---|---|
| Body | At rest (impending) | Sliding |
| Force | F ≤ μₛN | F = μₖN |
| Value | Larger | Smaller (μₖ < μₛ) |

## Check yourself

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

1. Limiting friction is:
   A. The normal reaction
   B. The maximum static friction, just when sliding is about to begin
   C. The friction during sliding
   D. Friction at zero load
   Answer: B. F_max = μs N at impending motion. (Key point: Limiting friction)

2. tan φ equals:
   A. N/F
   B. μk
   C. sin of the angle
   D. μs, with φ between N and the resultant R
   Answer: D. tan φ = F_max/N = μs. (Key point: Angle of friction)

3. Which is correct?
   A. μs depends on contact area
   B. μk is slightly less than μs
   C. They are equal always
   D. μk is greater than μs
   Answer: B. Sliding friction is slightly smaller than limiting static friction. (Key point: Static vs dynamic)

## Related in Applied Mechanics

- [Angle of friction; laws of static friction](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aangle-of-friction-laws-static-friction) — 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
- [Dynamic equilibrium; velocity and acceleration in polar](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Adynamic-equilibrium-polar-velocity-acceleration) — Applied Mechanics, chapter 9

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