by µµ

Physics is the science of universal laws and natural phenomena. Scientists have put in years of research to learn about the laws that govern nature and existence. These facts, theories, rules and laws are harnessed in reference tables. Reference Tables for physics supply the relevant axiomatic information on which advanced research depends heavily.

Purpose and examples of physics reference tables:

A very simple example of a reference table for physics is the List of Physical Constants. These include gravitational acceleration, speed of light in vacuum or sound in air, mass of the earth or Jupiter, the magnitude of 1 electrovolt, distance between the earth and the Sun, etc. These are facts that we cannot change, hard as we might try.

Other tables of reference are wavelengths and frequencies of electromagnetic waves in vacuum, indices of refraction, classification of matter, periodic elements (valancies and atomic weights), particles of standard model – a base for particle physics, formulae and equations for laws of electricity and electromagnetism, circuit theory, Heat Constants (melting, boiling points, heat of vaporization or fusion) and so on.

Potential difference = work (electrical energy)/charge

Speed = distance /time

Force = mass * acceleration

All of these are statements pinned in reference tables of various branches of physics.

Use of reference tables to connect physics with mathematics

Mathematical Physics is the area where mathematics is applied to solve problems in physics. Mathematical theorems, laws and properties shape theories and advanced concepts in physics. Since the laws of physics, that apply to this universe, its matter, energy and beyond, are based on laws or properties of mathematics, these two subject areas are very closely coupled. Advanced concepts in physics like string theory, wave theory, quantum mechanics, classical mechanics, and relativity depend heavily on mathematical reference tables. These are lists of mathematical functions, formulae, equations, constants, co-efficients, proofs, theorems, postulates, derivatives, integrals, bases, and so on.

Physics reference tables are with us today because of our scientists, who with their gifted intellect, persevered to understand the ways of the Divine.

Zero Vectors

Often we want to manipulate a point {a,b}, such as moving it, rotating it around a point, or extending it in the direction from origin (scaling). It helps greatly to think of a point {a,b} as a line from the Origin to {a,b}. When a point is thought of this way, we call it a vector.

Length of a Vector

The length of a vector is the distance from origin to the vector. If a vector is {a,b}, then by Pythagorean Theorem of a right triangle, its length is Sqrt[a^2+b^2]. Thus we define the length of a vector to be:

Length[{a,b}] := Sqrt[a^2+b^2]

Zero Vector: The vector {0,0} is interesting because it is the only vector whose length is 0. We give it a name the “zero vector”. It is special and useful in the same way the point {0,0} is also called Origin.

Vector Addition

A point {a,b} moved horizontally by c units and vertically by d units, will be at {a+c,b+d}. We can think of this as addition of two vectors {a,b} and {c,d}.

We define the addition of two vectors {a,b} and {c,d} as the sum of their components. We denote the vector addition operator as ?. That is:

{a,b} ? {c,d} := {a+c, b+d}

We define a vector addition because it is very useful. It simplifies discussion and expression. Think of a vector {a,b} as a arrow from the origin {0,0} to destination {a,b} on the coordinate system. Then, the sum of A and B is simply moving from origin by A’s components, then by B’s components, to end at {a+c,b+d}.

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