Dynamic equilibrium in physics

Dynamic equilibrium occurs when a system is in motion but maintains a steady speed and rotation.

In this state, all forces and torques acting on the system are perfectly balanced, preventing any acceleration or deceleration.

Static vs. Dynamic Equilibrium

When we hear the word "equilibrium," we often picture a motionless object. This describes static equilibrium.

However, equilibrium isn’t just about remaining still, there’s also a type that applies to moving objects, known as dynamic equilibrium.

Depending on the nature of the system, we can distinguish between two types:

• Dynamic equilibrium of a point mass
  A point mass is in dynamic equilibrium when it moves at a constant velocity. In other words, the net force acting on it is zero, yet the object continues moving without any change in speed or direction.

  Example: A car cruising at a steady speed on a straight road is in dynamic equilibrium because the engine’s thrust is exactly counteracted by friction and air resistance.

• Dynamic equilibrium of an extended body
  An extended body is in dynamic equilibrium when it moves and rotates at a constant rate, meaning neither its linear motion nor its angular motion changes over time.

  Example: A ceiling fan spinning at a fixed speed without speeding up or slowing down is in dynamic equilibrium.

Conditions for Dynamic Equilibrium

For an object to be in dynamic equilibrium, two key conditions, analogous to those for static equilibrium, must be met:

• Translational equilibrium
  The sum of all forces acting on the object must be zero: \[ \sum \vec{F} = 0 \] This ensures that the object maintains a constant velocity with no acceleration.
• Rotational equilibrium
  The sum of all torques about any point must be zero: \[ \sum \vec{M} = 0 \] This guarantees that the object’s angular velocity remains unchanged.

Dynamic equilibrium is a fundamental concept that can be observed everywhere in the physical world.

For instance, artificial satellites remain in dynamic equilibrium as they orbit Earth at a constant speed. The pull of gravity is exactly balanced by the centrifugal effect of their orbital motion.

Dynamic equilibrium highlights an important truth: stability and motion are not mutually exclusive. An object can be in perfect balance even while moving, as long as its linear and rotational velocities remain constant.

Mastering this concept is crucial in fields like mechanics and engineering.