Forces - Moments

If an object is fixed in place using a pivot (a shaft or other fixing that is designed to allow movement of the object), then you have the exact situation required for a turning force to arise. When an object is placed on something narrower, the narrow object can act as a pivot too, for example, a plank placed on a brick. Finally the edges or curved parts of objects can act as pivots too - take for example, a fork. Placed with the curved side uppermost, it is stable, however, placed with the curved side on the table, pressing downwards on the prongs will create a turning force that raises the handle.

The pivot is sometimes referred to as the fulcrum, especially in the context of levers.

When a force is applied to a pivoted object, if it is to one side or the other of the pivot, the object will experience a moment. If the magnitude of the moment is sufficient to overcome any frictional forces, then the object will turn around the pivot. The size of the moment depends on the size of the force applied and its perpendicular distance from the pivot. The equation for calculating a moment is simply the force multiplied by the distance. The SI unit of force is the newton; the SI unit for distance is meters, so the SI units for moments will be newton metres.

All pivoted systems obey the principle of moments. This tells us that if a pivoted object is not moving, the sum of the counterclockwise moments is the same as the sum of the clockwise moments. Questions on your exam paper will often ask you to work out the force or the distance that would be needed to balance a specific moment. Answering such questions is just a case of rearranging the equation that represents the principle of moments to isolate the term you are required to work out:

anticlockwise force x counterclockwise distance = clockwise force x clockwise distance

In some parts of the world, the circus is still very popular. Several circus acts utilize the principle of moments. Trapeze artists are one such group of performers. The trapeze is just an object that is fixed in place by a pivot, high in the big top tent. They can change the moment on the trapeze by altering the position of their center of gravity. Some of the more spectacular trapeze artists even use the principle of moments to reach the trapeze - they use a see-saw! One or more members of the troupe will stand on a platform and the trapeze performer stands on the end of a specially strengthened see-saw. The people on the platform jump down together and land on the end of the see-saw. The moment they create is larger than the one created by the single person on the other end, so the force moves the see-saw. As you know, when a force moves, work is done. This work done transfers the gravitational potential energy of the jumpers into kinetic energy, firing the performer upwards to reach their trapeze. There is lots of physics in operation at a circus.