Static equilibrium is a term used in physics to describe a situation in which the total forces acting on an object at rest add up to zero. In other words, the forces pulling the object in different directions balance out, causing the object to remain motionless. For an object to be in static equilibrium, it must also be in translational equilibrium and in rotational equilibrium, meaning that the external forces and external torques acting on the object must sum up to exactly zero.
In physics, forces of movement are often described in terms of vectors. A vector is an abstract mathematical concept used to represent both the direction and magnitude of a force. If a crate were being pulled a certain distance to the left, for example, the vector would indicate both the direction of the force and the distance the crate was pulled.
Newton’s first law of motion states that an object will remain at a constant velocity if the sum of vector forces on that object is zero. Objects at rest will stay at rest unless acted upon by a force, and objects in motion will, likewise, stay at the same velocity unless acted upon. The vector sum is also called the resultant force, or net force.
In a case of static equilibrium, forces are acting on an object, but the vector sum of all forces acting on that object is zero. This means that opposing vectors cancel each other out exactly, resulting in zero net force on the object. Although forces are present, the object remains motionless. To continue the example given above, if the crate were being pulled both left and right simultaneously with exactly the same amount of force and exactly opposing torque, all vectors would be opposed exactly to each other and the crate would not move. It would be in static equilibrium.
When the external forces acting on an object cancel each other out, the object is said to be in translational equilibrium, the first condition necessary for static equilibrium. The second condition is rotational equilibrium. In rotational equilibrium, the net torque, or rotational force, acting on the object must be zero. If, for example, the crate is being pulled left and right but is also being twisted around an axis, it would not be in static equilibrium, because torque would cause it to move. An equal and opposite force of torque would be required to set the crate in rotational equilibrium.