Moments — Quick Summary

Mr Toogood's Physics · Mechanics

AQA 3.4.1.2
M = Fd
Moment about a pivot
M = Fd
Couple (d = between forces)
ΣM_cw=ΣM_ccw
Principle of moments
N m
Units (torque)

Moments

Diagram defining the moment of a force as force times perpendicular distance from the pivot

Moment = force × perpendicular distance from the pivot to the line of action.

Moment = F × d (perpendicular)

The turning effect ("leverage") of a force about an axis — increased by a bigger force or a bigger perpendicular distance. Also called torque; units N m.

#1 source of error: "perpendicular distance" means to the force's line of action, not to its point of application. If a force isn't at 90° to the object, resolve it into a component perpendicular to it first.

Principle of moments

For an object in equilibrium: sum of clockwise moments = sum of anticlockwise moments, about the same point. A reliable 4-step method:

  1. Draw the weight — for a uniform object, through its exact centre.
  2. Choose a smart pivot — a point where an unknown force acts, so it drops out of the equation (d=0 there).
  3. Label each remaining force clockwise or anticlockwise.
  4. Resolve, or find the perpendicular distance for any force not acting at 90° to the object.

Couples

Two hands applying equal and opposite forces to turn a steering wheel, forming a couple

Equal, opposite forces on parallel (not shared) lines — pure rotation, no translation.

Two equal and opposite forces acting along parallel but different lines. Since they cancel as a resultant force, a couple only turns an object — it never causes translation.

Moment of a couple = F × d

Here d is the distance between the two lines of action, not to any pivot. Uniquely, the moment of a couple is the same about any point on the object. Examples: turning a steering wheel, twisting a tap, using a spanner on a nut.

Stability

An object tilted at increasing angles, showing when its centre of mass moves outside its base of support and it topples

Stable while the weight's line of action stays within the base of support.

Weight acts through the centre of mass. An object stays stable as long as a vertical line from the centre of mass falls within its base of support — once it falls outside, the weight's moment tips the object over instead of restoring it.

  • Wider base → more stable (needs a bigger tilt to topple).
  • Lower centre of mass → more stable, for the same reason.

Exam essentials

Key equations

  • M=Fd (moment about a pivot)
  • M=Fd (couple, d between forces)
  • ΣM_cw=ΣM_ccw

4-step method

  • Draw the weight through the centre.
  • Choose a smart pivot (removes an unknown).
  • Label each force cw/ccw.
  • Resolve any force not at 90°.

Common slips

  • Measure distance to the force's line of action, not its point of application.
  • Couples use the distance between the two forces — not to a pivot.
  • The centre of mass of a uniform regular solid is at its geometric centre.