Statics

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For static analysis in economics, see Comparative statics. For the technique of static correction used in exploration geophysics, see Reflection seismology.

Statics is the branch of mechanics that is concerned with the analysis of loads (force and torque, or "moment") acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment. When in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. Newton's second law

Where bold font indicates a vector that has magnitude and direction. F is the total of the forces acting on the system, m is the mass of the system and a is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration will be inversely proportional to the mass.

The summation of forces, one of which might be unknown, allows that unknown to be found. Likewise the application of the assumption of zero acceleration to the summation of moments acting on the system.

Here, M is the summation of all moments acting on the system, I is the moment of inertia of the mass and α = 0 the angular acceleration of the system.

The summation of moments, one of which might be unknown, allows that unknown to be found. These two equations together, can be applied to solve for as many as two loads (forces and moments) acting on the system.

From Newton's first law, this implies that the net force and net torque on every part of the system is zero. The net forces equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium. See statically determinate.

Dynamics (mechanics)

From Wikipedia, the free encyclopedia

For dynamics as the mathematical analysis of the motion of bodies as a result of impressed forces, see analytical dynamics.

Dynamics is a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.

Principles

Generally speaking, researchers involved in dynamics study how a physical system might develop or alter over time and study the causes of those changes. In addition, Newton established the fundamental physical laws which govern dynamics in physics. By studying his system of mechanics, dynamics can be understood. In particular, dynamics is mostly related to Newton's second law of motion. However, all three laws of motion are taken into account because these are interrelated in any given observation or experiment.

Force

From Newton, force can be defined as an exertion or pressure which can cause an object to accelerate. The concept of force is used to describe an influence which causes a free body (object) to accelerate. It can be a push or a pull, which causes an object to change direction, have new velocity, or to deform temporarily or permanently. Generally speaking, force causes an object's state of motion to change.^[1]

Newton's laws

Main article: Newton's laws of motion

Newton described force as the ability to cause a mass to accelerate. His three laws can be summarized as follows:

First law: If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.^[2]^[3]
Second law: The rate of change of linear momentum P of an object is equal to the net force F_net, i.e., dP/dt = F_net.
Third law: When a first body exerts a force F₁ on a second body, the second body simultaneously exerts a force F₂ = −F₁ on the first body. This means that F₁ and F₂ are equal in magnitude and opposite in direction.