Equilibrium
A body is truly in equilibrium when it has no tendency to turn or
move.
This means that:
When a body is in equilibrium:
and also:
It is easy to show
this using the light loaded beam of length L shown in Figure 1. Notice that F
1 will turn
the beam anticlockwise about the pivot (P) while F
2 will turn it clockwise.
Using
the principle of moments and taking moments about the pivot:
Balancing the vertical forces:
Notice the
minus sign since R acts in the opposite direction from F
1 and
F
2.
Further example
A more
complex example where there are three forces acting on the rod is shown below (Figure 2).
Using the principle of
moments and taking moments about the pivot:
Clockwise
moments = F1d1 + F2d2 = F3d3 = Anticlockwise
moments
Moments may be
taken about any point
(a) If we take moments about end A :
Anticlockwise
moments = LR/2 = [L/2 + d
1] F
1+ [L/2 + d
2] F
2 + [L/2 –
d
3] F
3 = Clockwise moments
(b) If we take moments about end B
:
Anticlockwise moments = [L/2 - d
1] F
1+ [L/2 - d
2] F
2 +
[L/2 + d
3] F
3 = LR/2 = Clockwise moments
Combining equations (a)
and (b) gives:
Clockwise moments = F
1d
1 + F
2d
2 =
F
3d
3 = Anticlockwise moments
The identical result that we obtained by
taking moments about the pivot.
