Home / Topics / Work, Energy & Power
Equilibrium types
Advanced
Stable, unstable and neutral equilibrium from the curvature of U.
At an equilibrium dU/dx = 0. If d²U/dx² > 0 it is stable (minimum), if < 0 unstable (maximum), if = 0 neutral (flat). Small displacements from stable equilibrium produce oscillations.
A ball on a hilltop is unstable; in a valley, stable.
Zero force alone doesn't tell stability.
In more detail
Equilibria are stable if small displacements lead to restoring forces, unstable if they lead to growing displacements, and neutral if the object stays where it is moved. These correspond to minima, maxima and flat regions of the potential energy.
Real-world uses
- A ball in a bowl is in stable equilibrium, while a ball on a hilltop is unstable.
- Engineers ensure that structures are stable under small disturbances.
- A cone balanced on its tip is in unstable equilibrium, while a cone resting on its base is in stable equilibrium.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How do I identify stable equilibrium?
A minimum in the potential energy curve is stable.
What is neutral equilibrium?
An object is in neutral equilibrium if it stays put when moved, such as a ball on a flat table.
What is neutral equilibrium?
A system with a flat potential energy curve, such as a ball on a flat table, which stays wherever it is put.
Related topics in Work, Energy & Power
Non-conservative forces · Force from potential energy · Potential energy curves · Conservation of mechanical energy · Energy conservation in free fall · Energy on a pendulum