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The purpose of science is to better understand the world in which we live. Understanding means that we know more than just memorizing a collection of simple facts. We want to know the underlying cause and effect relationships. Based on observation we see a high degree of regularity in our universe. It is reasonable to assume then that the universe is governed by certain underlying rules which are called laws of nature. Physical science tries to discover these laws and descibe them in a physical theory.
Physical theories are ways to represent dynamical systems in the most precise way possible, in order to allow prediction of the future states of a system, given knowledge about the present state. In general a physical theory consists of the following elements:
Dynamical systems can be either modelled as deterministic, one outcome possible, or stochastic, multiple outcomes possible each with a certain probability.
In classical physics the laws of nature are time reversable and deterministic, resulting in a state space where each subsequent state has a unique predecessor and a unique successor. The laws of nature together with the initial conditions determine the unique evolution of such a state space.
Classical physics is based on the famous force law of Newton $F=m\ddot{r}$, where $m$ is the mass of an object and $\ddot{r}$ the second derivative of position. A change of motion is the result of a change in the second derivative of position, acceleration caused by a force $F$. It follows that the initial conditions needed to predict the evolution requires two pieces of information: position, $r$ and the first derivative of position, velocity, $\dot{r}$. The initial conditions together with a force law determines the evolution of a classical mechanical system.
Does determinism implies perfect predictability ? The answer is: NO. There is randomness or uncertainty about the future even in a world with deterministic force laws. To illustrate this point, consider P and P' on the arc of a circle associated with the points Q and Q' (where Q is found by drawing a line from the top of the circle through P). Slight errors in the measurement of P produce big errors in the location of Q despite the fact that points on the horizontal line are uniquely determined by those on the circle. The position of P is a real number, but the typical real number can only be expressed as a decimal expansion consisting of an infinite string of digits with no systematic pattern to it, a random sequence. So, by its nature we could never find P exactly and therefore are always uncertain about Q.
Processes in nature that are extremely sensitive to the initial conditions are called nonlinear or chaotic systems. Processes that are less sensitive are called linear or deterministic systems. The errors in chaotic systems grow at an exponential rate.
From everyday life we know that we have the ability to distinguish objects from an environment. We observe an object at a distinct position in that environment. An instant later we are able to recognize that the position of the object has changed. We call this change a phenomenon or an event. We formulate this basic experience into an axiom for physics.
Each object occupies a unique set of positions in space at a certain instant of time. Each instant of time is followed by a next instant of time at which the object can occupy a different set of positions in space. This change in position with time is a physical phenomena and called the motion of the object.
Theory 
Major topic 
Concepts 
Classical mechanics  Newtonian mechanics, Lagrangian mechanics, Hamilton mechanics, Chaos theory, Fluid dynamics, Continuum mechanics  Dimension, Space, Time, Motion, Length, Velocity, Mass, Momentum, Force, Energy, Angular momentum, Torque, Conservation law, Harmonic oscillator, Wave, Work, Power 
Electromagnetism  Electrostatics, Electricity, Magnetism, Maxwell's equations,Optics  Electric charge, Current, Electric field, Magnetic field, Electromagnetic field, Electromagnetic radiation, Magnetic monopole 
Thermodynamics and Statistical mechanics  Heat engine, Kinetic theory  Boltzmann's constant, Entropy, Free energy, Heat, Partition function, Temperature 
Quantum mechanics  Path integral formulation, Schrodinger equation, Quantum field theory  Hamiltonian, Identical particles, Planck's constant, Quantum entanglement, Quantum harmonic oscillator, Wave function, Zeropoint ener 
Theory of relativity  Special relativity, General relativity  Equivalence principle, Fourmomentum, Reference frame, Spacetime, Speed of light 
To study physical objects and phenomena observation and measurement are crucial. Certain properties are identified. These properties are measured quantitatively and therefore also called physical quantities. A quantity is expressed by a single number and called a scalaror by a mathematical object consisting of a set of numbers in the case of a vectors or a tensor.
There are different set of numbers, such as: natural, integer, rational, real and complex number sets. All these number sets have imposed an ordering of its elements. Two other important properties of a number set is its density and scarity. We define a number set as dense if between any two numbers $A$ and $B$ there exists a number $C$ such that $A < B < C$. The rational numbers are dense. A number set is called complete or continuous if it contains no "holes". The real numbers are complete, the rational numbers not. We define a variable as: discrete (isomorphic with the natural numbers), dense (isomorphic with rational numbers) or continuous (isomorphic with real numbers). Physical variables are most often assumed to be continuous.
All measurement in physics are done by an (fictitious) observer assuming a certain geometry of space and time. This observer always measures by assuming a certain reference frame. A reference frame is a set of axes relative to practically rigid body in which an observer measures the position and distances of all points, as well as the orientation.
Different types of reference frames are defined
For studying the properties of physical objects and phenomena several fundamental quantities are defined. These quantities are measured (i.e. compared with a standard) in units which have a precise operational definition. For these units the standard metric system SI, System International, is used. In physics the following base quantities are defined to study the properties of physical phenomena:
Fundamental quantity 
Unit 
Symbol 
Lenght (L)  Meter  m 
Mass (M)  Kilogram  kg 
Time (T)  Second  s 
Electric current (Q)  Ampere  A 
Thermodynamic temperature ($\Theta$)  Kelvin  K 
Amount of substance  Mole  mol 
Luminous intensity  Candela  cd 
For each fundamental quantity a precise measurement procedure has been defined, Bureau International des Poids et Mesures.
In nature there are three important physical constants which provide natural dimensions and units (see Physical Measurement Laboratory):
Besides the base quantities there are derived quantities from the base quantities.
Physicists hold very strongly to the assumption that the laws of physics possess objective reality: the laws of physics are the same for all observers. One immediate consequence of this assumption is that a law of physics must take the same form in all possible systems of units that a prospective observer might choose to employ. The only way in which this can be the case is if all laws of physics are dimensionally consistent: i.e., the quantities on the left and righthand sides of the equality sign in any given law of physics are the same.
Power 
Prefix name 
Prefix symbol 
Scale 
$10^{24}$  yotta  Y  quadrillion 
$10^{21}$  zetta  Z  trilliard 
$10^{18}$  exa  E  trillion 
$10^{15}$  peta  P  billiard 
$10^{12}$  tera  T  billion 
$10^9$  giga  G  milliard 
$10^6$  mega  M  million 
$10^3$  kilo  k  thousand 
$10^2$  hecto  h  hundred 
$10^1$  deca  da  ten 
$10^{1}$  deci  d  tenth 
$10^{2}$  centi  c  hundredth 
$10^{3}$  milli  m  thousandth 
$10^{6}$  micro  $\mu$  millionth 
$10^{9}$  nano  n  milliardth 
$10^{12}$  pico  p  billionth 
$10^{15}$  femto  f  billiardth 
$10^{18}$  atto  a  trillionth 
$10^{21}$  zepto  z  trilliardth 
$10^{24}$  yocto  y  quadrillionth 
Scientific notation is the most reliable way of expressing a number to a given number of significant figures. In scientific notation, the power of ten is insignificant. So writing data 5.0 x $10^{1}$ means data in 2 significant figures (i.e. a number between 4.9 x $10^{1}$ and 5.1 x $10^{1}$) ,while 5 x $10^{1}$ means one significant figure (i.e. a number between 4 x $10^{1}$ and 6 x $10^{1}$).
When handling significant figures in calculations, two rules are applied:
Multiplication and division: round the final result to the least number of significant figures of any one term \[ \frac{{(15.03)(4.87)}} {{1.987}} = 36.8 \] The number is rounded to 3 significant figures, because least number of significant figures was found in the term, 4.87. The other terms, 15.03 and 1.987, each had 4 significant figures.
Addition and subtraction: round the final result to the least number of decimal places, regardless of the significant figures of any one term \[ \frac{\begin{align} 1&.003 \\ 1&.2 \\ 1&.484 \\ \end{align} } {{3.687}} \] rounds off to 3.7 since the least number of decimal places found in the given terms was 1
Although final answers should be expressed with an appropriate number of digits of accuracy, you should still keep all the digits for intermediate computations.