Dynamic equilibrium in physics describes an object moving at a constant velocity with zero net force and zero net torque acting on it. Unlike a book sitting still on a table, an object in dynamic equilibrium is in motion, but nothing about that motion is changing. No speeding up, no slowing down, no change in direction. The forces acting on it are perfectly balanced, so it coasts along in a straight line (or rotates at a steady rate) indefinitely.
The Two Conditions for Dynamic Equilibrium
For an object to be in dynamic equilibrium, two things must be true at the same time. First, all the external forces acting on it must cancel out to zero. In physics notation, that’s written as net F = 0. If forces act in two dimensions, this means the forces in the horizontal direction sum to zero and the forces in the vertical direction sum to zero, independently.
Second, all the external torques (twisting forces) must also cancel out to zero. Torque is what causes an object to spin faster or slower. When the net torque is zero, the object either doesn’t rotate at all or rotates at a perfectly constant rate. Both conditions together guarantee that nothing about the object’s motion is accelerating, whether that’s straight-line motion or rotation.
How Newton’s First Law Explains It
Dynamic equilibrium is really just Newton’s first law in action. That law states that every object remains at rest or moves in a straight line at constant speed unless a net external force acts on it. The key insight is that constant velocity is the natural state of things when forces balance. You don’t need a force to keep something moving. You only need a force to change how something moves.
This is where a common misconception creeps in. Many people assume that if something is moving, there must be a force pushing it forward. But in dynamic equilibrium, the object keeps moving precisely because no unbalanced force exists to stop it or speed it up. A hockey puck gliding across frictionless ice would be in dynamic equilibrium: it moves at a steady speed in a straight line, with no net force acting on it.
Static vs. Dynamic Equilibrium
Both types of equilibrium share the same mathematical requirements: net force equals zero and net torque equals zero. The difference is entirely about whether the object is moving.
- Static equilibrium: The object has zero velocity. It’s not moving or rotating. A bridge, a lamp hanging from the ceiling, or a book on a shelf are all in static equilibrium.
- Dynamic equilibrium: The object has a constant, nonzero velocity. It’s moving in a straight line at a steady speed, or rotating at a steady rate, with all forces and torques balanced.
In both cases, acceleration is zero. The only distinction is that static equilibrium is the special case where velocity also happens to be zero. Dynamic equilibrium is the broader case where velocity can be anything, as long as it isn’t changing.
Terminal Velocity: A Classic Example
One of the clearest real-world examples of dynamic equilibrium is a skydiver falling at terminal velocity. When you first jump from a plane, gravity pulls you downward and you accelerate. But as your speed increases, air resistance (drag) pushing upward grows stronger. At some point, the drag force exactly equals your weight. The net force becomes zero, your acceleration drops to zero, and you fall at a constant speed. That constant speed is terminal velocity, and it’s a textbook case of dynamic equilibrium.
NASA describes this balance simply: when drag equals weight, there is no net external force on the object, and it falls at a constant velocity as described by Newton’s first law. For a skydiver in a belly-down position, this happens at roughly 190 km/h (120 mph). The skydiver is clearly in motion, clearly experiencing large forces, but those forces perfectly cancel.
An Airplane in Cruise Flight
Commercial aircraft in level, constant-speed cruise provide another excellent example. Four forces act on a plane in flight: weight pulling it down, lift pushing it up, thrust pushing it forward, and drag pulling it backward. According to the Smithsonian National Air and Space Museum, when an airplane flies straight and level at a constant speed, lift balances weight and thrust balances drag. All four forces cancel in pairs, the net force is zero, and the plane is in dynamic equilibrium.
The moment the pilot increases thrust or enters a turn, the forces become unbalanced, acceleration occurs, and the plane leaves dynamic equilibrium. It only returns to equilibrium once a new steady state is reached, with all forces balanced again at the new speed or altitude.
Rotational Dynamic Equilibrium
Dynamic equilibrium applies to rotation too, not just straight-line motion. A rigid body is in rotational equilibrium when its angular acceleration is zero, meaning the sum of all external torques acting on it equals zero. If the object happens to be spinning while this condition holds, it spins at a constant rate forever (or until something changes).
Think of a ceiling fan running at a steady speed. The electric motor applies a torque that exactly matches the resistive torque from air drag and friction in the bearings. Net torque is zero, angular acceleration is zero, and the fan maintains a constant rotational speed. That’s rotational dynamic equilibrium. If you switched the fan to a higher setting, torque from the motor would temporarily exceed the resistive torque, the fan would accelerate, and once drag caught up at the new speed, equilibrium would be restored.
Why Zero Net Force Does Not Mean No Forces
A common point of confusion is thinking that equilibrium means no forces are present. In dynamic equilibrium, large forces can be acting on an object. A skydiver at terminal velocity experiences hundreds of newtons of gravitational force and hundreds of newtons of drag. A cruising airliner experiences millions of newtons of lift and weight. The forces are enormous, but they cancel perfectly, producing zero net force and therefore zero acceleration.
Another frequent mistake is assuming that if an object is accelerating, the force on it must be increasing. Research on student misconceptions in physics education has found this belief is widespread: students often think “acceleration implies increasing force.” In reality, any constant nonzero net force produces constant acceleration. And when that net force drops to zero, acceleration stops instantly, even though the object keeps moving at whatever velocity it had reached. That transition from accelerating to constant velocity is exactly the transition into dynamic equilibrium.
How to Recognize Dynamic Equilibrium
When you’re working through a physics problem or observing a real situation, check three things. Is the object moving? Is its speed constant? Is its direction constant? If all three answers are yes, you’re looking at dynamic equilibrium. The velocity vector isn’t changing in any way, which means acceleration is zero, which means the net force must be zero. From there, you can set up equations where all the forces in each direction sum to zero and solve for unknown quantities like tension, friction, or applied force.
If the object is moving in a circle at constant speed, that’s not dynamic equilibrium. Circular motion involves a continuously changing direction, which means there’s a centripetal acceleration and a net inward force. Constant speed alone isn’t enough. The velocity, which includes both speed and direction, must be constant.