S-Cool Revision Summary

S-Cool Revision Summary

Calculating moments

Factors affecting moments

When you push a door closed, it doesn't travel in a straight line - it turns around the hinges. This is an example of a moment (or torque).

So there are three things that are important:

  • The size of the force.
  • The direction of the force.
  • The distance from the force to the hinge.

Definition of Moments (or Torque)

"A moment is defined as a force multiplied by the perpendicular distance from the line of action of the force to the pivot."

Units: Nm. Symbol, M (or sometimes T)

Principle of Moments

For equilibrium:

The sum of the clockwise moments about a point = sum of the anticlockwise moments about that point.


If you have two forces (for instance, a couple of forces) acting on an object and the forces are:

  • parallel
  • in opposite directions
  • of equal size
  • not along the same line of action

...you have got a couple.

Definition of Moments diagram

Equilibrium Conditions

You need to check that two conditions are satisfied before you can say that something is in equilibrium.

  • The sum of the forces in any direction = 0. If this is satisfied, the object will have no linear acceleration (for instance, it won't accelerate in any direction).
  • The sum of the moments about any point (not just the pivot point) = 0. If this is satisfied, there is no angular (or circular) acceleration (for instance, the object won't rotate faster or slower.)

We write these two in short hand as:

Σ F = 0

Σ M = 0

Triangle of Forces

This is a quick way of finding out if the forces acting on an object are in equilibrium.

This object experiences three forces.

Triangle of Forces diagram

If it is in equilibrium then drawing accurate vector diagrams of each force one after the other will produce a closed triangle.

Centre of Gravity (and Centre of Mass)

Why is it useful?

When doing moment calculations you can say that all the weight of an object acts through the Centre of Gravity.

What's the difference between Centres of Gravity and Mass?

Centre of Gravity = the point where all the weight seems to be concentrated.

Centre of Mass = the point where all the mass seems to be concentrated.

Where can you find the Centre of Gravity?

For regular shapes it is the geometrical centre of the object - for example, the centre of a cube or a sphere.

For irregular shapes, hang the object from a point on its edge and the Centre of Gravity will end up vertically below the point you are hanging it from.