The concept of static equilibrium, more precisely static mechanical equilibrium, is used in physics to describe a steady state in which the relative position of the components of a system does not change with time. It doesn’t mean they don’t move, they can, what doesn’t change is the relative position between the components.

In other words, in the state of static equilibrium the system is at rest or its center of mass is moving with constant velocity.

This concept is implicit in the Law of Inertia, the first of Newton’s three laws:

Every body perseveres in its state of rest or uniform and rectilinear motion, unless it is compelled to change its state by forces impressed upon it.

Newton’s 1st Law or Law of Inertia

The most common definition of static equilibrium uses net force: An object is in static equilibrium when the sum of the forces acting on it (net or net force) is equal to zero. Both translational and torsional forces are taken into account and therefore an object is in static equilibrium if it is in both translational and rotational equilibrium.

Another broader definition defines the state of static equilibrium as that state of an object whose position in space has a potential energy gradient of zero. In this definition the object can move at a constant speed and implies that, although in our observation frame it may not appear, it is always possible to find a frame of reference with respect to which the object is stationary.

## Driving Forces and the State of Equilibrium

As defined, static equilibrium implies that the resultant of the forces acting on the object is zero, the forces continue to act, but there is equilibrium. To understand how forces can act on an object but remain in a state of equilibrium, it is necessary to understand what a driving force is and how it acts.

The effect on motion, according to Newton’s Second Law or Fundamental Law of Dynamics, is proportional to the magnitude of the force and occurs in the straight line in which the force is exerted. That is, driving forces are vector forces that are defined by a direction and a magnitude. When multiple forces are applied to an object, the resultant force is equal to the vector sum of all the forces, that is, the resultant force is equal to the resultant vector. If the net force is of zero magnitude, then the object is in static equilibrium.

In the mathematical expression, the net force, as stated by Newton in his second law, is:

Where F is the force, m is the mass, v is the velocity and you are the time. In words, the resultant force is equal to the momentum differential (m×v) in a given time interval. Then the object will be in a state of equilibrium if the momentum becomes zero during this time interval.

If the object’s mass remains constant, the above equation can be expressed as the product of the mass and the acceleration experienced by the object:

Where F is the net force, m is the mass, which remains constant, and a is the acceleration. Since F is zero if the object is in static equilibrium, an object of constant mass can be said to be in equilibrium when the sum of the forces acting on it produces zero acceleration.

If you read the previous paragraphs carefully, static equilibrium does not necessarily imply that the object does not move. If an object in vacuum is given a small push, it will start moving and will remain moving forever and at a constant speed, as there is no force that slows or accelerates it (for example, a moving car on the street). a road is slowed down by gravity and friction.). Therefore, the object can move and be in static equilibrium at the same time, as long as the net force acting on it is zero, which fulfills the Law of Inertia.

### torsional forces

So far we have talked about the translational forces acting on the object. But in addition to translational equilibrium, static equilibrium state requires rotational equilibrium. Rotational equilibrium is reached when all torsional forces cancel and their resultant is zero.