# Mechanics

In physics, mechanics includes all theories explaining the behaviour of matter. Mechanics can also refer to the practical subjects of creating and maintaining machines.

Each physical theory of mechanics has these three ingredients.

- A system of kinematics by which the configuration and trajectory of the system being studied is described. For example, a set of locations in a cartesian coordinate system, at specified times, can provide a means of describing the motion of an object.

- A description of how a force or forces act.

- A mathematical statement of a relationship prevailing on the kinematic measurements and forces. Such statement is often called a principle. F = ma for example, is a principle of Newtonian Mechanics.

Principles are developed from the knowledge of routine observations and from deliberately planned experiments. As a mechanical theory becomes established, an extensive body of mathematical deduction develops. This yields further opportunities for verification of principles. The mathematical deductions and verifications can address extreme cases. Thus F = ma is true for many problems of engineering while it fails for objects moving at high speeds such as photons.

## Examples

- In Newtonian mechanics, matter takes the form of bodies or particles each of which has a mass m and position in space. Time is measured independently from spacial dimensions. A body can be subjected to a force F or multiple forces. Principles of the theory include the statement F = ma, a being the acceleration of the body.
- In thermal mechanics, matter is typically a fluid with intensive properties such as temperature T and extensive properties such as volume V within a container. Force is measured as pressure P. An early princple of the theory was the ideal gas law, PV = nRT; n being the number of moles of the gas and R, the Universal Gas Constant.

## Unification

As understanding of theories expands, they become unified. Principles are simplified and generalized. For example, the earliest form of statistical mechanics was built upon Newtonian Mechanics with the addition of statistical concepts. That theory yielded the statement PV = NkT; N being the number of molecules of a gas and k the Boltzmann constant. Given Avogadro's number, this equation is equivalent to the Ideal Gas Law. This demonstrates a connection between Newtonian Mechanics and thermal mechanics. PV = nRT is no longer a principle of thermal mechanics but is found to be understandable from Newtonian Mechanics with the addition of statistical concepts.

Unification of theories of mechanics has been a central preoccupation of theoretical physicists. Grand Unification is the problem of unifiying the theories of the four fundamental forces currently known: gravity, strong and weak nuclear interactions and electromagnetic interaction.