Statics and Torque

# The First Condition for Equilibrium

OpenStaxCollege

### Learning Objectives

- State the first condition of equilibrium.
- Explain static equilibrium.
- Explain dynamic 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

Note that if net 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

[link] and [link] illustrate situations where 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 [link] and [link] 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 [link], the ice hockey stick remains motionless. But in [link], 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.

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

# Section 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 .

# Conceptual Questions

What can you say about the velocity of a moving body that is in dynamic equilibrium? Draw a sketch of such a body using clearly labeled arrows to represent all external forces on the body.

Under what conditions can a rotating body be in equilibrium? Give an example.

## 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