Designing levers - turning effects and moments

Force and distance

We have seen from the previous examples of working with levers that the two quantities which need to be taken into account are the size of force acting and the length from the pivot.

More precisely we need to take account of:

• The sizes of the forces acting F₁ and F₂
• The perpendicular lengths between the line of action of each force and the pivot point L₁ and L₂

The line of action of a force is exactly what the name suggests: The direction or line along which the force acts. In the diagram, F₁ acts along a line vertically upwards: so does F₂ – but along a different line.

Both of the forces F₁ and F₂ produce a turning effect on the lever:

• F₁ tends to turn the lever in a clockwise direction.
• F₂ tends to turn the lever in an anti-clockwise direction.

The size of these turning effects can be calculated.

Calculating turning effects

Here's a precise way of writing it out, so that every term is just a number:

turning effectnewton metre = perpendicular lengthmetre × forcenewton

You can also express it rather concisely as:

turning effect = perpendicular length × force

The moment

The turning effect is called the moment of the force and is measured in newton metres.

For the example given above (given that the lever is balanced): clockwise moment = anti-clockwise moment, so L₁ × F₁ = L₂ × F₂.

This law of balancing actually follows from the principle of conservation of energy.

If you are interested in seeing how one bit of physics can be used to explain another, take a look at the following expansion nugget.