Cases of equilibrium:

What are cases of equilibrium?

Sol.: As a result of the acting forces, the body may be having one of the following states:

(1) The body can move in any one direction:

If the body may move in any one direction it means that there is some resultant force acting on it. A small consideration will show that if the body is at rest or in equilibrium, the resultant force causing movement should be zero. Or H and V must be zero.

ΣH = 0       and       ΣV = 0

(2) The body can rotate about itself without moving:

It means that there is single resultant force acting on it with no resultant force. A small consideration will show that if the body is at rest or in equilibrium, the moment of couple which causes rotation should be zero. Or we can say that

ΣM = 0

(3) The body can move in any one direction, and at the same time it can also rotate about itself:

It means that there is resultant force and resultant couple acting on it. A small consideration will show that if the body is to be at rest or in the equilibrium, the resultant force causing movement and the resultant moment of couple causing rotation should be zero. That is

ΣH = 0,     ΣV = 0     and         ΣM = 0

(4) The body can be completely at rest:

It means that there is neither resultant force nor a couple acting on it. A small consideration will show that in this case the following condition are satisfied already:

ΣH = 0,      ΣV = 0 and           ΣM = 0