Types of Equilibrium

Translational equilibrium. When a body's linear momentum stays constant, the net force acting on it is zero:

meaning the vector sum of every individual force acting on the body, $\vec F_1+\vec F_2+\vec F_3+\cdots+\vec F_n$, is exactly zero. If the individual forces act along several different directions, this vector-sum condition is usually applied by resolving every force into convenient horizontal and vertical components and demanding the resultant vanish separately along each direction — giving, in general, both a horizontal-equilibrium condition and a vertical-equilibrium condition that must both hold simultaneously.

Rotational equilibrium. Likewise, when a body's angular momentum stays constant, the net torque acting on it, about any chosen point, is zero:

meaning the vector sum of every individual torque, $\vec\tau_1+\vec\tau_2+\vec\tau_3+\cdots+\vec\tau_n$, producing possibly different senses of rotation, is exactly zero.

Mechanical equilibrium, as introduced in §5.3, requires both of these conditions to hold together: $\vec F_{net}=0$ and $\vec\tau_{net}=0$. Since both force and torque are vector quantities, the correct sign convention (e.g. anticlockwise torques positive, clockwise negative) must always be applied consistently when adding them.

With this foundation, several distinct, precisely-defined kinds of equilibrium can now be distinguished from one another (summarised in the reference table below): static equilibrium, where linear and angular momentum are not merely constant but exactly zero (the body is genuinely motionless — neither translating nor rotating); dynamic equilibrium, where linear and angular momentum are constant but need not be zero (e.g. a body coasting at constant velocity, or spinning steadily); and, cutting across both of these, the three stability classes based on how the body responds to a small disturbance:

• Stable equilibrium — the body returns to its original equilibrium position if slightly disturbed and released; on disturbance its center of mass rises slightly and its potential energy, which was at a minimum, increases. …