Here, we are going to look at forces acting at different points, and in this situation even if the forces balance there may be a resultant moment.

Figure 11.11

Figure 11.11 shows a tray on a smooth surface being pushed equally hard at opposite corners.

The resultant force on the tray is clearly zero, but the resultant moment about its center point, G, is

The tray will start to rotate about its center and so it is clearly not in equilibrium.

Note:

You could have taken moments about any of the corners, A, B, C or D, or any other point in the plane of the paper and the answer would have been the same, Pa anticlockwise.

So we now tighten our mathematical definition of equilibrium to include moments.

For an object to remain at rest (or moving at constant velocity) when a system of forces is applied, both the resultant force and the total moment must be zero.

To check that an object is in equilibrium under the action of a system of forces,
you need to check two things:

(i) that the resultant force is zero;

(ii) that the resultant moment about any point is zero. (You only need to check
one point.)