# First Condition

## The first condition of equilibrium is that the net force in all directions must be zero.

#### Key Points

• There are two conditions that must be met for equilibrium.

• The same conditions apply both to static equilibrium and dynamic equilibrium.

• If net force is zero, then net force along any direction is zero.

#### Terms

• A rotational or twisting effect of a force; (SI unit newton-meter or Nm; imperial unit foot-pound or ft-lb)

• Motion of a body on a linear path, without deformation or rotation, i.e. such that every part of the body moves at the same speed and in the same direction; also (in physics), the linear motion of a body considered independently of its rotation.

• A physical quantity that denotes ability to push, pull, twist or accelerate a body which is measured in a unit dimensioned in mass × distance/time² (ML/T²): SI: newton (N); CGS: dyne (dyn)

#### Figures

1. ##### Static Equilibrium

This motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case.

2. ##### Dynamic Equilibrium

This car is in dynamic equilibrium because it is moving at constant velocity. There are horizontal and vertical forces, but the net external force in any direction is zero. The applied force Fapp between the tires and the road is balanced by air friction, and the weight of the car is supported by the normal forces, here shown to be equal for all four tires.

## First Condition of Equilibrium

An object that is motionless or undergoes no translational and rotational acceleration is said to be in equilibrium. That is, the net force and net torque on the object is zero in all directions. For an object to truly be in equilibrium, two conditions must be met.

The first condition states that the net force acting on the object must be zero. This means that for each axis of motion, the forces acting along that particular axis must sum to 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

$net F_{x} = 0$ and $net F_{y} = 0$.

Figure 1 and Figure 2 illustrate situations where $net F = 0$ for both static equilibrium (motionless), and dynamic equilibrium (constant velocity). In Figure 1, the motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case. In Figure 2, the car is in dynamic equilibrium because it is moving at constant velocity. There are horizontal and vertical forces, but the net external force in any direction is zero. The applied force $F_{app}$ between the tires and the road is balanced by air friction, and the weight of the car is supported by the normal forces, here shown to be equal for all four tires.

But remember, for true equilibrium, condition 1 is only half the picture.

#### Key Term Glossary

acceleration
The amount by which a speed or velocity increases (and so a scalar quantity or a vector quantity).
##### Appears in these related concepts:
Acceleration
the rate at which the velocity of a body changes with time
##### Appears in these related concepts:
axis
An imaginary line around which an object spins (an axis of rotation) or is symmetrically arranged (an axis of symmetry).
##### Appears in these related concepts:
constant velocity
Motion that does not change in speed nor direction.
##### Appears in these related concepts:
dynamic
Changing; active; in motion.
##### Appears in these related concepts:
equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
##### Appears in these related concepts:
equilibrium
The state of a body at rest or in uniform motion, the resultant of all forces on which is zero.
##### Appears in these related concepts:
Equilibrium
A state of rest or balance due to the equal action of opposing forces.
##### Appears in these related concepts:
force
A physical quantity that denotes ability to push, pull, twist or accelerate a body which is measured in a unit dimensioned in mass × distance/time² (ML/T²): SI: newton (N); CGS: dyne (dyn)
##### Appears in these related concepts:
Force
A force is any influence that causes an object to undergo a certain change, either concerning its movement, direction or geometrical construction.
##### Appears in these related concepts:
friction
A force that resists the relative motion or tendency to such motion of two bodies in contact.
##### Appears in these related concepts:
motion
A change of position with respect to time.
##### Appears in these related concepts:
net force
The combination of all the forces that act on an object.
##### Appears in these related concepts:
normal
A line or vector that is perpendicular to another line, surface, or plane.
##### Appears in these related concepts:
normal force
Any force acting normal, to a surface, or perpendicular to the tangent plane.
##### Appears in these related concepts:
static
Fixed in place; having no motion.
##### Appears in these related concepts:
static equilibrium
the physical state in which all components of a system are at rest and the net force is equal to zero throughout the system
##### Appears in these related concepts:
torque
A rotational or twisting effect of a force; (SI unit newton-meter or Nm; imperial unit foot-pound or ft-lb)
##### Appears in these related concepts:
Torque
Something that produces or tends to produce torsion or rotation; the moment of a force or system of forces tending to cause rotation.
##### Appears in these related concepts:
velocity
A vector quantity that denotes the rate of change of position with respect to time, or a speed with a directional component.
##### Appears in these related concepts:
Velocity
The rate of change of displacement with respect to change in time.
##### Appears in these related concepts:
weight
The force on an object due to the gravitational attraction between it and the Earth (or whatever astronomical object it is primarily influenced by).