The principle of moments

If an object is balanced, the total clockwise moment about a pivot is equal to the total anticlockwise moment about that pivot. This is called ‘the principle of moments’.

If the object is balanced: total clockwise moment = total anticlockwise moment. The diagrams show two examples of balanced objects where there is no rotation.

There is a cross section of a trough with a ball at the lowest point inside.
A plank sits on a pivot like a see-saw. Boxes sit at each end of the plank, with two equal arrows pointing downwards from the boxes.

A ball at the bottom of a trough

A balanced see-saw

An object in equilibrium will not turn or accelerate - there is no overall (resultant) force and the clockwise moments are equal to the anticlockwise moments.

For a balanced object, you can calculate:

  • the size of a force, or
  • the perpendicular distance of a force from the pivot

Example

A parent and child are at opposite ends of a playground see-saw. The parent weighs 750 N and the child weighs 250 N. The child sits 2.4 m from the pivot. Calculate the distance the parent must sit from the pivot for the see-saw to be balanced.

child's moment = force × distance

250 N × 2.4 m = 600 Nm

Parent's moment = child's moment

Rearrange M = F \: d to find d for the parent:

d = \frac{M}{F}

Then calculate using the values:

d = \frac{600~Nm}{750~N}

d = 0.8~m