Moments

The turning effect of a force is called the moment, M, of the force.

Turning effect of the force simply means the tendency of the force to cause the object to turn around a point.

You can calculate it by multiplying the force and the perpendicular distance from the line of action of force to the pivot point (or fulcrum).

M = Fd

Definition: The moment of force is defined as the product of the force and the perpendicular distance between the force and the fulcrum.

Eg.1

The 4 N force will cause the stick to turn anticlockwise about the pivot point [the fulcrum]. We say that the 4 N force creates anticlockwise moments about the fulcrum.

M = 4 N x 0.4 m = 1.6 Nm anticlockwise

Eg 2.

This 5 N force will create a clockwise moment about the pivot point.

M = Fd

M =5 N x 0.50 m = 2.5 Nm clockwise

For an object (such as the bar in the exaple) to be in equilibrium two things must apply:

1) The principle of moments must apply.

The principle of moments states that for equilibrium, the sum of the moments in the clockwise direction equals the sum of the moments in the anticlockwise direction.

Σ Anticlockwise moments = Σ Clockwise moments

2) the sum of forces in one direction must equal the sum of forces in the opposite direction.

Eg 3.

At what distance, d, on the opposite side to the 4 N force can I place the 5 N force so that the ruler remains in equilibrium?

From the principle of moments

Anticlockwise moments = Clockwise moments

4 N x 0.25m = 5 N x d

1 Nm = 5d Nm

d = 1/5 = 0.2 m