Newtonian Mechanics is derived from two principles:
- the motion of tangible bodies: position, velocity, acceleration
- what causes it - force on the object.
Newton's description leads naturally to two new quantities, which prove to be globally constant
- momentum - the "quantity of motion" as Newton called it
- energy - the quantity of work that can be done
Whereas momentum was very much a part of Newton's thinking, energy is a concept that arose ~160 years after Newton and is highly relevant to our civilization today.
Since extended bodies can rotate as well as move, these concepts are generalized to include
- angular position and its velocity and acceleration
- torque - force that acts to rotate an object about an axis
Together the above 6 concepts constitute Newtonian Mechanics, which underlies the fields of mechanical and civil engineering and when extended to flowing fluids (ie. liquids and gasses) the fields of aeronautics and hydrodynamics as well. In this WIKI we will group them into four major areas:
- Motion of a particle in 3-dimensional space
- Energy
- Momentum and Force
- Angular Momentum (including the description of angular motion)
In principle, Newtonian Mechanics can be derived from only Newton's Laws (which include ∑F=ma) and the calculus of motion. However, energy and momentum follow from these assumptions and prove to be extremely useful ways to think about the world.
Modern Extensions of Newtonian Mechanics
Modern physics (since 1800) offers four major extensions of Newtonian Physics:
Statistical Mechanics and Heat - properties of huge numbers of objects (e.g. gas particles) including heat (which is closely related to their average energy)
Electricity, Magnetism, and Light
Quantum Mechanics - Small objects no longer behave in a classical fashion: measuring the position and velocity of small changes it, and Relativity - fundamental changes to the idea of all the fundamental concepts of Newtonian mechanics: mass, energy, and the very geometry of space (length and time are in fact not separate physical quantities, and space itself no longer behaves according to the predictions of plane geometry and trigonometry).
Relativity - As speeds approach that of light, the usual distinction between length and time breaks down as they transform into one another differently for differently moving observers according to the laws of Special Relativity. Around massive objects, space-time is no longer Euclidian but becomes distorted according to the laws of General Relativity.