$$\require{cancel}$$

9.1: The First Condition for Equilibrium

The first condition necessary to achieve equilibrium is the one already mentioned: the net external force on the system must be zero. Expressed as an equation, this is simply

$net \, F = 0$

Note that if net $$F$$ is zero, then the net external force in any direction is zero. For example, the net external forces along the typical x- and y-axes are zero. This is written as

$net \, F_x \, and \, F_y = 0$

Figuress $$\PageIndex{1}$$ and $$\PageIndex{2}$$ illustrate situations where $$net \, F = 0$$ for both static equilibrium (motionless), and dynamic equilibrium (constant velocity).

However, it is not sufficient for the net external force of a system to be zero for a system to be in equilibrium. Consider the two situations illustrated in Figures $$\PageIndex{3}$$ and $$\PageIndex{4}$$ where forces are applied to an ice hockey stick lying flat on ice. The net external force is zero in both situations shown in the figure; but in one case, equilibrium is achieved, whereas in the other, it is not. In Figure $$\PageIndex{3}$$, the ice hockey stick remains motionless. But in Figure $$\PageIndex{4}$$, with the same forces applied in different places, the stick experiences accelerated rotation. Therefore, we know that the point at which a force is applied is another factor in determining whether or not equilibrium is achieved. This will be explored further in the next section.

PhET Explorations: Torque

Investigate how torque causes an object to rotate. Discover the relationships between angular acceleration, moment of inertia, angular momentum and torque.

Summary

• Statics is the study of forces in equilibrium.
• Two conditions must be met to achieve equilibrium, which is defined to be motion without linear or rotational acceleration.
• The first condition necessary to achieve equilibrium is that the net external force on the system must be zero, so that $$F = 0$$.

Glossary

static equilibrium
a state of equilibrium in which the net external force and torque acting on a system is zero
dynamic equilibrium
a state of equilibrium in which the net external force and torque on a system moving with constant velocity are zero