Classical mechanics

Classical Mechanics is the study of the effects of forces on bodies. It can be divided into two parts: Newtonian Mechanics, named after Sir Isaac Newton,and Relativity, developed by Albert Einstein.

Newtonian Mechanics

Motion

Any body that moves from one point to another has an average velocity(v_av) which is a measure of the rate of change of displacement($\Delta$x) with time. In equation form:

$v=\Delta x/\Delta t\,\!$ ,

The instantaneous velocity is then the limit of the average as the time interval($\Delta$ t) approaches zero:

$v=dx/dt\,\!$,

In a one dimensional system the term speed could be used instead of velocity however in more dimensions the difference between a vector quantity (like velocity which has a magnitude and a direction) and a scalar quantity (such as speed which only has a magnitude) is very important.

If the velocity of a body changes with time the body has acceleration(a). Acceleration is related to velocity in the same way as velocity is to displacement:

$a=\Delta v/\Delta t\,\!$ , and

$a=dv/dt\,\!$,

Newton's laws of motion

Newton's laws of motion help to analyze the principles of dynamics, the relationship of motion to the forces that cause it. These three laws were first published in 1687 in Philosophiae Naturalis Principia Mathematica.

The first law states that:

A body acted on by no net force moves with constant velocity and zero acceleration.

This means that a body in motion has a property called inertia, a tendency to keep moving unitl another force causes it to stop.

The second law states that:

If a net force acts on a body, the body accelerates. The force equals the mass of the body multiplied by the acceleration.

This relation of force and motion is a fundamental law of nature. If there is a constant net force acting on an object it's velocity will continue to increase at a constant rate of acceleration.

The third law states that:

If body A exerts a force on body B, then body B exerts a force on body A. This force will have an equal magnitude and opposite direction.

This is less formally stated as; every action has an equal and opposite reaction. It's important to remember these two forces act on different bodies.