State the principle of moments.

The principle of moments states that for a body in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.

In other words, if a body is not moving or rotating, the total clockwise moments acting on it must be balanced by the total anticlockwise moments. This principle is based on the fact that moments are a measure of the turning effect of a force, and that a body in equilibrium is one where the net turning effect of all forces acting on it is zero.

To apply the principle of moments, we need to choose a point about which to calculate the moments. This point is called the pivot or fulcrum. We then identify all the forces acting on the body and their distances from the pivot. The moment of a force is calculated by multiplying its magnitude by its perpendicular distance from the pivot.

For example, consider a uniform beam of length 4m and weight 100N supported horizontally at its midpoint by a pivot. If a person of weight 600N stands 1m from one end of the beam, what is the weight of the beam acting at the pivot?

We can choose the pivot as the midpoint of the beam, and apply the principle of moments:

Clockwise moments = 600 x 3 = 1800 Nm
Anticlockwise moments = 100 x 2 + W x 2 = 200 + 2W Nm
Equating these moments, we get:
1800 = 200 + 2W
W = 800N

Therefore, the weight of the beam acting at the pivot is 800N.