# Physics - Principles

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/s2

## 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
name description examples
scalar A scalar quantity has a continuous range of values in one dimension time, energy
vector A vector is a quantity with magnitude and direction. linear velocity or moment
rotor A rotor is a quantity with magnitude, direction, and position. rotational velocity
about a fixed axis or force along line of action
motor A motor is the sum of two or more rotors, which can be represented as a wrench or twist about a certain screw. the sum of arbitrary system of forces is, in
general, not a force but a combination of force and moment.
quaternion

Representing the orientation of a 3D solid body and rotations on it requires 3 dimensions, but because of its special properties, explained here, it is better to represent it as a quaternion or matrix.

A related concept in 'n' dimensions is a spinor

orientation of a solid body
matrix

Some quantities such as the rotational inertia of a 3D body are best represented as an array of numbers.

A related concept in 'n' dimensions is a tensor

inertia tensor

### Related Topics

Other pages on this part of the site ask how we use these principles to model the real world.

 Physics and Maths The relationship between mathematics and Physics. Modeling This discusses the different approaches to modeling the physical world. Given that it is not practical to simulate every atom and every particle in the part of the physical world being simulated. We therefore need to make practical decisions about what assumptions to make in order to make the model practical. Solid objects Since the atoms are locked together, we can treat a solid body as a single entity, we need to consider: Kinematics Dynamics Forces Collision detection and response Jointed Systems Relaxation methods A way to model deformable objects Equations model Numerical methods

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