﻿ Mechanics Map - Static Equilibrium

# Static Equilibrium

Objects in static equilibrium are objects that are not accelerating (either linear acceleration or angular acceleration). These objects may be stationary, such as a building or a bridge, or they may have a constant velocity, such as a car or truck moving at a constant speed on a straight patch of road. Because this high rise building is stationary with no acceleration, the members and overall structure are in equilibrium. Image by Jakembradford CC-BY-SA 4.0. Assuming that this truck is maintaining a constant speed and direction, this truck is in equilibrium because its velocity is not changing over time. Public Domain image by Klever.

Newton's Second Law states that the force exerted on an object is equal to the mass of the object times the acceleration it experiences. Therefore, if we know that the acceleration of an object is equal to zero, then we can assume that the sum of all forces acting on the object is zero. Individual forces acting on the object, represented by force vectors, may not have zero magnitude but the sum of all the force vectors will always be equal to zero for objects in equilibrium. Engineering statics is the study of objects in static equilibrium, and the simple assumption of all forces adding up to zero is the basis for the subject area of engineering statics.

 $\sum \vec{F}=m\vec{a}$ $a=0$ $\sum \vec{F}=0$

Equilibrium follows a similar pattern for angular accelerations. The rotational equivalent of Newton's Second Law states that the moment exerted on an object is equal to the moment of inertia of that object times the angular acceleration of the object. If we know the angular acceleration of an object is equal to zero, then we know the sum of all moments acting on the object is equal to zero.

 $\sum \vec{M}=I\vec{\alpha}$ $\alpha=0$ $\sum \vec{M}=0$