PlanetPhysics/Equilibrium and Statics

In common speech, anything is likely to be called static if it is not changing. While a particle at rest or with unchanging position is considered to be static, we also consider a particle to be static if its velocity is not changing. This point of view is expressed by Newton's laws of motion according to which a state of uniform motion of a particle with any velocity is simply natural and does not require the action of any force, independently of whether the velocity is zero or has a large magnitude. If, then, the particle is not accelerated, there is no resultant force acting upon it. This does not preclude the possibility that the particle is subject to the action of two or more forces whose vector sum or resultant is zero. Such a set of forces is said to be in equilibrium. It is the study of sets or systems of forces in equilibrium that constitutes the subject of statics.

In speaking of the state of rest or the state of motion of a particle or a body, we need to explain with respect to what it is at rest or in motion. It is found that Newton's laws of motion do not hold with respect to every arbitrary system of coordinates. If we deal only with particles or bodies whose velocities are considerable less than the velocity of light, however, Newton's laws of motion do hold with a remarkable degree of accuracy provided all positions are determined with respect to an inertial system of coordinates. An inertial system of coordinates is any system which is either at rest relative to the "fixed" stars, or is moving with a constant velocity but without any rotation relative to the fixed stars. Any static particle or body, subject to a system of forces in equilibrium, may be considered to be at rest relative to some inertial system of coordinates. For many purposes, we may consider a set of axes fixed with respect to the earth to be an inertial system. This seems a rather reasonable approximation when we consider that it requires a year for the earth to traverse its orbit, and that the earth rotates about the axis through its poles with only half the angular velocity with which the hour hand of a clock revolves. For certain problems, however, particularly those involving large velocities or large displacements, large errors may be introduced by treating axes fixed relative to the earth as inertial axes. Particles and bodies at rest relative to the earth as inertial axes. Particles and bodies at rest relative to the earth may for nearly all present engineering purposes be considered to be at rest relative to an inertial system.


 * derivative of the Public domain work of [Broxon].