Equilibrium in physics is a state in which the relevant physical quantities remain constant in time according to the conditions being considered, with mechanical equilibrium specifically requiring that the net force and net torque on a body are both zero. Translational equilibrium requires the vector sum of all external forces to equal zero, written Sigma F = 0. Rotational equilibrium requires the net torque about an appropriate point or axis to equal zero, written Sigma tau = 0.
An object in mechanical equilibrium can be stationary, which is called static equilibrium, or it can move with constant velocity, which is dynamic equilibrium. Equilibrium does not necessarily mean that no forces are acting. Multiple forces can act simultaneously and cancel vectorially. For example, a book resting on a table experiences downward gravitational force and upward normal force, while remaining in equilibrium because their resultant is zero. Equilibrium is therefore a condition concerning net effects rather than the absence of interactions.
Static equilibrium occurs when an object remains at rest in a chosen inertial reference frame and has no net acceleration. For a rigid body, this requires both translational and rotational equilibrium. A suspended object can have several forces acting on it, such as tension, gravity, and air resistance, but if the vector sum is zero and the torque sum is zero, its position and orientation remain constant.
Static equilibrium is central to structural engineering because bridges, buildings, beams, cranes, shelves, and supports must withstand applied loads without accelerating or rotating. Engineers construct free body diagrams to identify external forces and moments and then solve equilibrium equations. For a planar rigid body, three independent scalar equilibrium equations are commonly available: the sum of horizontal forces is zero, the sum of vertical forces is zero, and the sum of torques about a selected point is zero. These equations provide the basis for calculating unknown support reactions and loads in many statics problems.
Dynamic equilibrium occurs when a system continues moving while relevant macroscopic quantities remain constant. An object travelling at constant velocity in a straight line has zero acceleration and therefore zero net force, even though it may have substantial kinetic energy. A car travelling at constant speed on a straight level road can be in translational equilibrium if driving force balances resistive forces.
A rotating object can similarly have constant angular velocity when net torque is zero, although it can still possess angular momentum and rotational kinetic energy. Dynamic equilibrium should not be confused with a situation in which nothing is happening. In many physical and chemical systems, opposing processes continue simultaneously while their net macroscopic rates cancel. Equilibrium therefore concerns balance of rates, forces, or changes depending on the physical context.
In rotational equilibrium, the choice of reference point for calculating torque can simplify the analysis. Torque from a force is represented by tau = r cross F, with magnitude tau = rF sin theta, where r is the displacement from the chosen origin to the point of application and theta is the angle between r and F. A force whose line of action passes through the chosen pivot produces zero torque about that pivot.
If clockwise and anticlockwise torques balance, the object has no angular acceleration. However, calculating torques about different points must remain consistent because the full vector condition for rotational equilibrium is that the net torque is zero. The ability to choose a convenient pivot is particularly useful in beam, ladder, lever, and support problems because forces acting through that point then contribute no torque to the selected equation.
Equilibrium can be stable, unstable, or neutral depending on how the system responds to small disturbances. In stable equilibrium, a small displacement produces forces or torques that tend to return the system toward its original state. A ball at the bottom of a bowl is a simple idealised example. In unstable equilibrium, a small disturbance tends to move the system farther from its original position, as with a ball balanced at the top of a hill.
In neutral equilibrium, a small displacement leaves the system in another equilibrium position, as with an ideal ball on a horizontal surface. Potential energy provides a useful framework for conservative mechanical systems. Stable equilibrium generally corresponds to a local minimum of potential energy, unstable equilibrium to a local maximum, and neutral equilibrium to a region where potential energy does not change with displacement. Real systems can be more complicated because friction, constraints, nonconservative forces, and multiple degrees of freedom affect stability.
Fluid systems also exhibit equilibrium. Hydrostatic equilibrium occurs when a fluid is stationary and pressure gradients balance body forces such as gravity. The hydrostatic equation dp divided by dz = minus rho g describes this balance for a fluid of constant density under uniform gravity. An atmosphere can approach hydrostatic balance even though pressure and density vary substantially with altitude. Objects immersed in fluids can reach equilibrium when buoyancy balances weight and any other forces.
A floating object is therefore an example of mechanical equilibrium involving a fluid pressure field. Chemical equilibrium has a related but distinct meaning in which forward and reverse reaction rates become equal under specified conditions, so concentrations remain macroscopically constant despite ongoing molecular activity. Thermal equilibrium occurs when systems have no net heat transfer due to temperature differences. These forms of equilibrium share the idea of balance but use different physical quantities and conditions.
Equilibrium analysis depends on the system boundary and reference frame. Forces internal to a system cancel in pairs when considering the total momentum of an isolated system, while external forces determine the acceleration of the system's centre of mass. A body may be in equilibrium relative to one accelerating reference frame only if appropriate fictitious forces are included in the analysis.
In an inertial frame, Newton's second law provides the direct relationship Sigma F = ma, so equilibrium requires a = 0. For extended rigid bodies, torque equilibrium must also be considered because zero net force alone does not prevent angular acceleration. A pair of equal and opposite forces can produce zero net force but a nonzero couple and therefore cause rotation. This is why force balance alone is insufficient for rigid body equilibrium.
Equilibrium is an idealisation that provides a powerful starting point for analysing real systems, but real systems can undergo slow deformation, vibration, thermal expansion, creep, fatigue, or other changes even when simplified equilibrium equations predict zero net force and torque. Structural equilibrium does not guarantee structural safety because material strength, buckling, fracture, fatigue, and dynamic loading must also be considered. Likewise, a mathematically balanced chemical system can be sensitive to changes in temperature, pressure, or composition.
The central principle is that equilibrium means no net change in the variables relevant to the defined system and conditions. In mechanical problems this normally means zero translational and rotational acceleration, expressed through force and torque balance. Understanding equilibrium therefore requires identifying the system, selecting an appropriate reference frame, listing relevant interactions, and distinguishing static balance from dynamic, thermal, fluid, or chemical forms of equilibrium.
