# 9.1 The first condition for equilibrium

 Page 1 / 3

## 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.

What is meant by dielectric charge?
what happens to the size of charge if the dielectric is changed?
omega= omega not +alpha t derivation
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
displacement in easy way.
binding energy per nucleon
why God created humanity
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
why electromagnetic induction is not used in room heater ?
room?
Abrar
What is position?
What is law of gravition
what is magnetism