These pages explain the standards and conventions used in the physics pages on this site. It introduces the types of physical quantities and their possible mathematical representations

- Physical Quantities
- Dimensions
- Matter
- Forces
- Symmetry and conservation laws

- Mathematical Representations
- Scalar
- Vector.
- Rotor.
- Motor
- Quaternion
- Matrix

# Physics Quantities

When studying physics we are concerned with Dimensions, Matter, Forces, Symmetry and conservation laws so we will consider these in turn:

## Dimensions

In classical physics there are 3 dimensions in space and one one time. These dimensions are independent of each other and infinitely long in both directions. As far as we know they are continuous. in the 3 dimensions of space there is no preferred orientation so, if we call these dimensions x,y and z, any direction is as good as any other as a basis for these dimensions provided they are mutually perpendicular. Coordinate systems are explained here.

The units of space are metres, and time is seconds.

## Matter

The world is made up from particles, fermions (such as electrons, neutrons and protons) and bosons (particles which make forces such as photons). In classical mechanics mass relates to forces by gravity (attracts other matter) and inertia (resistance to change in motion). In special relativity mass is related to energy.

The units of mass are kg.

## Forces

Forces are the only way for matter to interact with other matter, if forces did not exist then every piece of matter would move at constant speed, independently of all other matter. things would just pass through other things, no structures would exist and the world would be a very uninteresting place. The known types of forces are electo-magnetism, weak nuclear, strong nuclear and gravitational.

The units of Newtons are kg m/s^{2}

## Symmetry and conservation laws

The laws of physics are the same regardless of our position when we do an experiment, or the time that we do an experiment, or the direction that we are facing or the speed we are traveling when we do the experiment. From these symmetries come the conservation laws such as energy and momentum as explained here.

# Maths Representations

The above physical quantities above may be represented by various combinations of the following entities. For example the state of a 3D solid body may be represented by:

- linier position - 3D vector
- angular position - Quaternion
- momentum - 3D vector
- angular velocity - rotor