MOMENT OF A FORCE

1. The moment of a force

If a force is applied to the end of an object whose other end is attached to a pivot or hinge, the force will tend to rotate the object about the pivot, called the FULCRUM, Thus, a force can, in certain circumstances, have a turning effect. We call this effect the MOMENT OF THE FORCE ().


The moment depends on the size of the force, F, and the perpendicular distance, d, from the fulcrum to a line along the direction of the force vector (). Moments are expressed in units of NEWTON METRES (N·m). The direction of the rotation resulting from a moment is either clockwise or anticlockwise. Clockwise moments are regarded as positive, while anticlockwise moments are negative.

2. Levers

Levers are simple machines () that utilise the moment of a force.

Referring to the diagram on the left, the applied force, F (sometimes called the "effort") applies a clockwise moment Fy at a distance y from the fulcrum. Placed at a distance x on the left hand side of the fulcrum, we have a mass m, applying a force mg (the "load") having an anticlockwise moment mgx, where g is the acceleration due to gravity. This system will be in equilibrium, that is, there will be no motion, when the clockwise and anticlockwise moments have the same magnitude (numerical value): Fy = mgx. This is simply a specific example of the LAW OF MOMENTS.

The distance y is called the LEVER ARM of the force F about the fulcrum. Similarly, the distance x is the lever arm of the load mg about that fulcrum.

The photo on the left, below, shows three kitchen gadgets that operate on the principle of levers (top: pincers, middle: tongs, bottom: garlic press), each operating on a different arrangement of fulcrum, load and effort.


2. Conditions for equilibrium

A body will be in mechanical equilibrium if (a) it does not change its state of lateral motion and, (b), it does not rotate.

In order for a body not to rotate, the law of moments applies:

Law of Moments
"A body will be in equilibrium if the algebraical sum of the moments about any point is zero."



Note that the law of moments is not sufficient for defining the equilibrium of a body, as TWO conditions must apply:

  1. The vector sum of all forces acting on the body must be zero; and
  2. the algebraic sum of the moments about any point must be zero (law of moments).

3. Mechanical advantage

The MECHANICAL ADVANTAGE, MA, of a machine is the ratio of the load and the applied force (effort). In the case of the lever described above, the mechanical advantage is mg/F. It is also the ratio of the lever arms of the effort and load respectively, that is, y/x.

The mechanical advantage is therefore a factor which tells us how much the input force is multiplied by the machine.

4. Additional questions