Equilibrium — Core Principles
Core Principles
Equilibrium is a fundamental concept in physics describing a state where an object's motion remains constant. This means its linear velocity and angular velocity do not change. For an object to be in complete equilibrium, two conditions must be met: first, the net external force acting on it must be zero (translational equilibrium), ensuring zero linear acceleration.
Second, the net external torque acting on it must be zero (rotational equilibrium), ensuring zero angular acceleration. \n\nEquilibrium can be classified as static (object at rest) or dynamic (object moving with constant velocity).
Furthermore, static equilibrium can be stable (returns to original position after displacement), unstable (moves further away after displacement), or neutral (finds a new equilibrium position after displacement).
Solving equilibrium problems typically involves drawing free-body diagrams, resolving forces into components, choosing a strategic pivot point, and applying the conditions and to form a system of equations.
Important Differences
vs Dynamic Equilibrium
| Aspect | This Topic | Dynamic Equilibrium |
|---|---|---|
| State of Motion | Object is at rest (linear velocity $v=0$, angular velocity $\omega=0$). | Object is in motion (linear velocity $v \neq 0$ and/or angular velocity $\omega \neq 0$). However, these velocities are constant. |
| Acceleration | Linear acceleration $a=0$, angular acceleration $\alpha=0$. | Linear acceleration $a=0$, angular acceleration $\alpha=0$. (This is the commonality - zero acceleration). |
| Net Force | $\Sigma \vec{F} = 0$ | $\Sigma \vec{F} = 0$ |
| Net Torque | $\Sigma \vec{\tau} = 0$ | $\Sigma \vec{\tau} = 0$ |
| Example | A book resting on a table, a bridge standing still. | A car moving at a constant speed on a straight road, a satellite in a stable orbit. |