Until now the particle model has provided a reasonable basis for the analysis of the situations you have met.

In examples like the see-saw however, where turning is important, this model is inadequate because the forces do not all act through the same point.

In such cases you need the rigid body model in which an object, or body, is recognised as having size and shape, but is assumed not to be deformed when forces act on it.

Suppose that you push a tray lying on a smooth table with one finger so that the force acts parallel to one edge and through the center of mass (Figure 11.4).

Figure 11.4

The particle model is adequate here: the tray travels in a straight line in the direction of the applied force.

If you push the tray equally hard with two fingers as in Figure 11.5, symmetrically either side of the center of mass, the particle model is still adequate.

Figure 11.5

However, if the two forces are not equal or are not symmetrically placed, or as in Figure 11.6 are in different directions, the particle model cannot be used.

Figure 11.6

The resultant force is now zero, since the individual forces are equal in magnitude but opposite in direction.

What happens to the tray?

Experience tells us that it starts to rotate about G. How fast it starts to rotate depends, among
other things, on the magnitude of the forces and the width of the tray. The rigid body model allows you to analyse the situation.

(Ref: Cambridge International AS and A Level Mathematics by Sophie Goldie, Series Editor: Roger Porkess, Hodder Education)