First Condition

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

Learning Objective

Identify the first condition of equilibrium

Key Points

There are two conditions that must be met for an object to be in equilibrium.
The first condition is that the net force on the object must be zero for the object to be in equilibrium.
If net force is zero, then net force along any direction is zero.

Terms

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

Full Text

First Condition of Equilibrium

For an object to be in equilibrium, it must be experiencing no acceleration. This means that both the net force and the net torque on the object must be zero. Here we will discuss the first condition, that of zero net force.

In the form of an equation, this first condition is:

$F_\text{net} = 0$.

In order to achieve this conditon, the forces acting along each axis of motion must sum to zero. For example, the net external forces along the typical x- and y-axes are zero. This is written as

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

The condition $F_\text{net} = 0$ must be true for both static equilibrium, where the object's velocity is zero, and dynamic equilibrium, where the object is moving at a constant velocity.

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

Person in Static Equilibrium

This motionless person is in static equilibrium.

Below, 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 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.

A Car in Dynamic Equilibrium

This car is in dynamic equilibrium because it is moving at constant velocity. The forces in all directions are balanced.

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