 Statics

Statics studies mechanical equilibrium: configurations in which the relevant forces and torques balance. For a rigid body at rest in an inertial frame, the conditions are $\sum \mathbf{F}=0$ and $\sum {\mathbf{\tau }}_O=0$, with all torques calculated about the same point $O$.

A horizontal beam carrying a downward load illustrates why both equations are necessary. Vertical force balance fixes the sum of the support reactions, while torque balance determines how the load is divided between supports. Equilibrium alone does not imply dynamical stability: a perfectly upright inverted pendulum satisfies force and torque balance but falls after a sufficiently small disturbance.

Statics is a branch of mechanics that deals with the analysis of forces and moments acting on objects in equilibrium. It focuses on understanding how these forces affect the structure and configuration of stationary bodies. In statics, the primary condition for equilibrium is that the sum of all forces and the sum of all moments (torques) acting on a body must be zero.