Equilibrium conditions

The conditions for equilibrium to exist are that the sum of the forces and the sum of the torques acting on a given system must be zero.

A system is in equilibrium if the sum of forces and sum of torques are zero.
Statics is the branch of Mechanics that is dedicated to the study of equilibrium conditions , indicating the factors necessary for a structure or any body to be balanced.

1st equilibrium condition: the sum of forces

The first necessary condition for a given body to be in equilibrium is that the sum of all forces acting on it must be zero . From this definition arise the ideas of static and dynamic equilibrium .

Equilibrium is static when the net force on the body is zero and the body is at rest, that is, it has no velocity. When an object performs uniform rectilinear motion , there is no acceleration , so according to Newton’s second law , there is no net force. Since the force is zero and the object has constant velocity, the body is said to be in dynamic equilibrium.

2nd equilibrium condition: the sum of the torques

Torque , also called the moment of a force , is the vector quantity related to the rotation of a system. This quantity is defined by the product of the force applied perpendicularly at a given point in the system by the lever arm, which corresponds to the distance between the point of force application and the axis of rotation.

T = Fx

For a system to be in equilibrium, it is necessary that there is no rotation, therefore, the sum of the torques acting on the system must be zero.

In the simulator above, it is possible to organize the system according to the masses of the objects and the distances to the axes of rotation so that there is balance.


The best example of application of these concepts is civil construction, in which infinite possibilities of assembling structures must obey the equilibrium conditions. Another application example is the cranes used for filming. This equipment must contain a counterweight at the opposite end of the camera to ensure the professional’s balance and movement.

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