# 9.1 The first condition for equilibrium

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## Learning objectives

By the end of this section, you will be able to:

• 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

$\text{net}\phantom{\rule{0.25em}{0ex}}\mathbf{F}=0$

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

$\text{net}\phantom{\rule{0.25em}{0ex}}{F}_{x}=0\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\text{and}\phantom{\rule{0.25em}{0ex}}{F}_{y}=0$

[link] and [link] illustrate situations where $\text{net}\phantom{\rule{0.25em}{0ex}}F=0$ 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 [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.

## Phet explorations: torque

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 $\text{net}\phantom{\rule{0.25em}{0ex}}\mathbf{F}=0$ .

## 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.

#### Questions & Answers

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