---
title: "Force, couple and moment with sketch"
subject: "Applied Mechanics"
chapter: 3
key: "semester_1/applied_mechanics:force-couple-moment-sketch"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/force-couple-moment-sketch
site: BCT Engineering
---

# Force, couple and moment with sketch

Applied Mechanics · Chapter 3: Forces acting on particle and rigid body

- Asked in: 2067 Asoj, 4 marks
- Video: [Couple Moments | Mechanics Statics | (Learn to solve any question)](https://www.youtube.com/watch?v=uV4QDXd0ARM) — Question Solutions
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/force-couple-moment-sketch
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-3

## Question

Describe force, couple and moment with sketch.

## Short answer

Force is a push or pull tending to change motion, a vector with magnitude and direction. Moment is the turning effect of a force about a point, M = F × d. A couple is a pair of equal, opposite, parallel forces producing pure rotation, M = F × d.

## Answer

#### Force
A force is the action of one body on another that changes, or tends to change, the state of rest or motion of the body. It is a vector with magnitude, direction and point of application. Unit: newton (N).

#### Moment of a force
The moment of a force about a point (or axis) is the turning effect of the force about that point. M = F × d, where d is the perpendicular distance from the point to the line of action of the force (the moment arm). In vector form, M_O = r × F. Unit: N·m. By convention, anticlockwise moments are taken as positive.

```text
                 | F
                 v
  O o------------+
     <--- d --->
  (moment centre)        M_O = F × d  (clockwise here)
```

#### Couple
A couple is a pair of equal, opposite and parallel forces whose lines of action are different. It has no resultant force, only a turning effect, M = F × d, where d is the perpendicular distance between the forces.

```text
     F  ^                 F at A and −F at B
        |    d            M = F × d  (clockwise here)
    A   o-----------o B
                    |
                    v F
```

| Quantity | Force | Moment | Couple |
|---|---|---|---|
| Effect | Translates (and may rotate) | Rotation about a point | Pure rotation |
| Depends on point | Only its line of action matters (sliding vector) | Yes | No (free vector) |
| Unit | N | N·m | N·m |

## Check yourself

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

1. What is the moment of a force about a point?
   A. F × d, where d is the perpendicular distance from the point to the line of action
   B. F × the length of the body
   C. F + d
   D. F divided by d
   Answer: A. Vector form M_O = r × F; it measures turning effect about O. (Key point: Moment of a force)

2. Which describes a couple?
   A. Equal, opposite, parallel forces on different lines of action; no resultant force
   B. Two equal forces along the same line
   C. A single force with a moment
   D. Two forces at right angles
   Answer: A. A couple has only turning effect, M = F × d. (Key point: Couple)

3. Which statement is true?
   A. A force's moment depends on the reference point; a couple's moment does not
   B. A couple's moment depends on the point; a force's doesn't
   C. Neither depends on the point
   D. Both depend on the point
   Answer: A. A couple is a free vector. (Key point: Dependence on point)

4. Which quantities define a force?
   A. Magnitude, direction and point of application
   B. Magnitude only
   C. Magnitude and unit
   D. Direction and moment
   Answer: A. A force is a vector with magnitude, direction and point of application; unit N. (Key point: Force as vector)

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