Turning effects of forces

When a force acts on an object, it can cause the object to turn or rotate about a point or axis. This turning effect is fundamental in understanding how objects balance, rotate, and remain stable.

Centre of Gravity

The centre of gravity of an object is the point at which its entire weight appears to act, regardless of the orientation of the object. For regular, symmetrical objects made of uniform material, the centre of gravity is at the geometric centre. For irregular objects, it can be found by suspension or calculation.

A minimalist illustration showing a regular rectangle with a dot at its geometric center labeled 'Centre of Gravity'. Next to it, an irregular shape is suspended from a point, with a vertical dashed line passing through the suspension point and a dot where several such lines intersect, labeled 'Centre of Gravity'. Keep the design clean and modern.

Definition

The centre of gravity of an object is the point at which the entire weight of the object may be considered to act.

Moment of a Force

A force can cause an object to rotate about a pivot. The moment (or turning effect) of a force about a point is a measure of its tendency to cause rotation about that point.

A simple, clean diagram of a horizontal beam pivoted at one end (labeled 'Pivot'). A force arrow labeled 'F' acts downward at the other end. A dashed line shows the perpendicular distance 'd' from the pivot to the line of action of the force. Minimalist style, modern UI.

Definition

The moment of a force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action of the force.

Formula
Moment=F×d\text{Moment} = F \times d

where FF is the force (in newtons, N) and dd is the perpendicular distance from the pivot to the line of action of the force (in metres, m).

The SI unit of moment is the newton metre (N m).

Important

Always measure the distance dd as the perpendicular distance from the pivot to the line of action of the force.

Principle of Moments

When an object is in equilibrium (not rotating), the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.

Couples and Torque

A couple consists of two equal and opposite forces whose lines of action do not coincide. A couple produces rotation only, without causing any resultant force (no linear motion).

A minimalist diagram showing a horizontal bar with two equal arrows: one pointing up on the left end, one pointing down on the right end. Both arrows are labeled 'F'. The distance between the arrows is labeled 'd'. No pivot is shown. Clean, modern style.

Definition

A couple is a pair of equal and opposite forces acting on a body, but not along the same line, producing rotation only.

The torque (or moment) of a couple is the product of one of the forces and the perpendicular distance between their lines of action.

Formula
Torque of a couple=F×d\text{Torque of a couple} = F \times d

where FF is the magnitude of one force, and dd is the perpendicular distance between the lines of action of the forces.

Exam Tip

When calculating the torque of a couple, use the perpendicular distance between the forces, not from a pivot.

Summary

  • The centre of gravity is the point where the weight acts.
  • The moment of a force measures its turning effect about a point.
  • A couple produces rotation only; its torque is given by force × perpendicular distance between forces.
  • The SI unit for moment and torque is newton metre (N m).
Equilibrium of forces →

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