# Physics/Synopsis
## Force

    Force Symbol Mathematical Formula Opposing Force $F_{-}$ $-F$ Gravity Force $F_{g}$ $G{\frac {Mm}{r^{2}}}$ Motion Force $F_{a}$ $ma=m{\frac {v}{t}}={\frac {p}{t}}$ Pressure Force $F_{A}$ ${\frac {F}{A}}$ Elastic Force $F_{x}$ $-kx$ Circulation Force $F_{r}$ $mvr=pr$ Centripetal Force $F_{c}$ $m{\frac {v^{2}}{r}}$ Electrostatic Force $F_{q}$ ${\frac {q_{+}q_{-}}{r^{2}}}$ Electromotive force $F_{E}$ $qE$ Electromagnetomotive Force $F_{B}$ $\pm qvB$ Electromagnetic Force $F_{EB}$ $q(E\pm vB)$

## Motion
### Linear Motion

    O ----> O
    Distance$s$$vt$ Time$t$$t$ Speed$v$${\frac {s}{t}}$ Accelleration$a$${\frac {v}{t}}$ Force$F$$m{\frac {v}{t}}$ Work$W$$Fs$ Energy$E$${\frac {W}{t}}$
    O
    O
    Distance$s$$h$ Time$t$$t$ Speed$v$${\frac {h}{t}}$ Accelleration$a$${\frac {h}{t^{2}}}$ Force$F$$mg$ Work$W$$mgh$ Energy$E$${\frac {mgh}{t}}$
* Non-Uniform linear motion
    Distance$s$$(v_{o}+at)t$ Time$t$$t$ Speed$v$$v_{o}+at$ Accelleration$a$${\frac {\Delta v}{\Delta t}}$ Force$F$$m{\frac {\Delta v}{\Delta t}}$ Work$W$$Ft(v_{o}+at)$ Energy$E$$F(v_{o}+at)$

### Non Linear Motion

    Distance$s(t)$$\int v(t)dt$ Time$t$$t$ Speed$v(t)$$v(t)$ Acceleration$a(t)$${\frac {d}{dt}}v(t)$ Force$F(t)$$m{\frac {d}{dt}}v(t)$ Work$W(t)$$F\int v(t)dt$ Energy$E(t)$${\frac {F}{t}}\int v(t)dt$

### Circular Motion

* Complete full circle
    Distance$s$$2\pi r$ Time$t$$t$ Speed$v$$r{\frac {2\pi }{t}}=r\omega$ Acceleration$a$${\frac {r\omega }{t}}$ Angular spped$\omega$${\frac {2\pi }{t}}=2\pi f={\frac {v}{r}}$ Frequency$f$${\frac {1}{t}}$ Force$F$$m{\frac {r\omega }{t}}$ Work$W$$pr\omega$ Energy$E$${\frac {pr\omega }{t}}$
* Circle's arc
    Distance$s$$r\theta$ Time$t$$t$ Speed$v$$r{\frac {\theta }{t}}$ Acceleration$a$${\frac {r\theta }{t^{2}}}$ Force$F$$m{\frac {r\theta }{t^{2}}}$ Work$W$$pr{\frac {\theta }{t}}$ Energy$E$${\frac {pr\theta }{t^{2}}}$

### Momentum
#### Characteristics

    $F=ma=m{\frac {v}{t}}={\frac {p}{t}}$
    $p=mv=Ft$

#### Momentum of a mass

    Speed$v$$v$ Mass$m$$m$ Momentum$p$$mv=Ft$ Force$F$$ma=m{\frac {v}{t}}={\frac {p}{t}}$ Work$W$$Fs=Fvt=pv$ Energy$E$$Fv=Fat=pa$

#### Momentum of a relativistic mass

    Speed$v$$\gamma ={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}$ Mass$m$$m_{o}(\gamma -1)$ Momentum$p$$mv$ Energy$E$$pv$

#### Momentum of a massless quanta

    Speed$v$$C=\lambda f$ Mass$m$$h=p\lambda$ Energy$E$$pv=pC=p\lambda f=hf$ Momentum$p$${\frac {h}{\lambda }}$ Wavelength$\lambda$${\frac {h}{p}}={\frac {C}{f}}$

#### Momentum of an electric charge in circle

    Equilibrium$QvB=p{\frac {v}{r}}$ Speed$v={\frac {Q}{m}}Br$ Radius$r={\frac {p}{QB}}$

#### Momentum of atom's free electron

    Equilibrium$hf=hf_{o}+{\frac {1}{2}}mv^{2}$ Speed$v={\sqrt {{\frac {2}{m}}(hf-hf_{o})}}={\sqrt {{\frac {2}{m}}(nhf_{o})}}$ With $f>f_{o}=nf_{o}$ to have $v>0$

#### Momentum of a bind electron

    Equilibrium$nhf=mvr2\pi$ Speed$v={\frac {1}{2\pi }}{\frac {nhf}{mr}}$ Radius$r={\frac {1}{2\pi }}{\frac {nhf}{mv}}$ Potential Energy Level n$n=2\pi {\frac {mv}{hf}}$

### Wave
#### AC electrical sinusoidal wave generator

An interaction of 2 electromagnets creates an AC electricity that has amplitude varies sinusoidally
    $v(t)=ASin(\omega t+\theta )$

#### LC sinusoidal wave generator

Series LC operates at equilibrium satisfy wave equation
    ${\frac {d^{2}}{dt^{2}}}i(t)=-{\frac {1}{T}}i(t)$
that has root of a sinusoidal wave function
    $i(t)=ASin\omega t$
    $\omega ={\sqrt {\frac {1}{T}}}$
    $T=LC$

#### Electromagnetic sinusoidal wave generator

A coil of N turns operates at equilibrium satisfy wave equation
    $\nabla ^{2}E(t)=-\omega E(t)$
    $\nabla ^{2}B(t)=-\omega B(t)$
that has root of a sinusoidal wave function
    $E(t)=ASin\omega t$
    $B(t)=ASin\omega t$
    $\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f$
    $T=\mu \epsilon$

#### Wave Characteristics

    Distance$s$$\lambda$ Time$t$$t$ Speed$v$${\frac {\lambda }{t}}$ Angular speed$\omega$$2\pi f$ Frequency$f$${\frac {1}{t}}$ Sinusoidal wave equation$f^{''}(t)$$-\omega f(t)$ Sinusoidal wave function$f(t)$$ASin\omega t$

#### Wave types

    Wave2 dimensional sinusoidal wave3 dimensional sinusoidal plane wave Wave oscillation equation${\frac {d^{2}}{dt^{2}}}f(t)=-\omega f(t)$ Wave function $f(t)=ASin\omega t$ $E(t)=ASin\omega t$ $B(t)=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f$ $T=\mu \epsilon$

## Electricity
### Electricity Types

    Electricity types Definition Mathematical Formula Source DC ElectricityElectricity that provides constant voltage over time$v(t)=V$Electrolysis, Electrochemcial Cell, PhotonVoltaic AC ElectricityElectricity that provides sinusoidal changing voltage over changing time$v(t)=VSin\omega t$Electromagnetic induction

### DC & AC Response

* Resistor circuit
    CharacteristicsDCAC Voltage$V=IR$$v=iR$ Current$I={\frac {V}{R}}$$i={\frac {v}{R}}$ Resistance$R={\frac {V}{I}}$$R={\frac {v}{i}}$ Power provided$P_{V}=IV$$P_{V}=iv$ Power Loss$P_{R}=I^{2}R(T)={\frac {V^{2}}{R(T)}}$$P_{R}=i^{2}R(T)={\frac {v^{2}}{R(T)}}$ Power delivered$P=P_{V}-P_{R}$ Reactance$X_{R}=0$ Impedance$Z_{R}=X_{R}+R=R$ Phase$0$
* Capacitor circuit
    CharacteristicsDCAC Voltage$V=QC={\frac {W}{Q}}$$v={\frac {1}{C}}\int idt$ Charge$Q={\frac {V}{C}}$ Capacitance$C={\frac {V}{Q}}$ Current$I={\frac {Q}{t}}$$i=C{\frac {dv}{dt}}$ Power provided$P_{V}=IV=({\frac {Q}{t}})({\frac {W}{Q}})={\frac {W}{t}}$$p={\frac {1}{2}}Cv^{2}$ Reactance $X_{C}(t)={\frac {v}{i}}$ $X_{C}(j\omega )={\frac {1}{j\omega C}}$ $X_{C}(\omega \theta )={\frac {1}{\omega C}}\angle -90$ Impedance $Z_{C}(t)=X_{C}+R_{C}$ $X_{C}(j\omega )={\frac {1}{j\omega C}}+R_{C}$ $X_{C}(\omega \theta )={\frac {1}{\omega C}}\angle -90+R\angle 0$ Phase$Tan\theta ={\frac {1}{\omega T}}$ Time Constant$T=CR_{C}$
* Inductor circuit
    CharacteristicsDCAC Magnetic Field Strength$B=LI$ Current$I={\frac {B}{L}}$ Inductance$C={\frac {B}{I}}$ Current$I={\frac {Q}{t}}$ Power provided$P_{V}=IV=({\frac {B}{l}})({\frac {W}{Q}})={\frac {W}{t}}$ Reactance $X_{L}(t)={\frac {v}{i}}$ $X_{L}(j\omega )=j\omega L$ $X_{L}(\omega \theta )=\omega L\angle 90$ Impedance $Z_{C}(t)=X_{C}+R_{C}$ $X_{C}(j\omega )=j\omega L+R_{L}$ $X_{C}(\omega \theta )=\omega L\angle 90+R\angle 0$ Phase$Tan\theta =\omega T$ Time Constant$T={\frac {L}{R_{L}}}$
* Electric Decay
    ${\frac {d}{dt}}i=-{\frac {1}{T}}i$ $i=Ae^{-{\frac {1}{T}}t}$$T={\frac {L}{R}}$ ${\frac {d}{dt}}v=-{\frac {1}{T}}v$ $v=Ae^{-{\frac {1}{T}}t}$$T=RC$
* Electric Oscillation
    Modes of OscillationOscillation equationWave FunctionAngular SpeedOscillation Time ConstantOscilation ConstantDecay Constant 'Decay Time Constant Electric decay current sinusoidal wave oscillation ${\frac {d^{2}}{dt^{2}}}i=-2\alpha {\frac {d}{dt}}i-\beta i$$i=A(\alpha )Sin\omega t$$\omega ={\sqrt {\beta -\alpha }}$$T=LC$$\beta ={\frac {1}{T}}$$\alpha =\beta \gamma$$\gamma =RC$ Electric peak current sinusoidal wave oscillation $Z_{L}=-Z_{C}$ $Z_{t}=R$ $i(\omega =0)=0$ $i(\omega =\omega _{o})={\frac {v}{2}}$ $i(\omega =00)=0$$\omega _{o}={\sqrt {\frac {1}{T}}}$$T=LC$ Electric current sinusoidal wave oscillation ${\frac {d^{2}}{dt^{2}}}i=-{\frac {1}{T}}i$$i=ASin\omega t$$\omega ={\sqrt {\frac {1}{T}}}$$T=LC$ Electric current sinusoidal standing wave oscillation $Z_{L}=-Z_{C}$$V_{L}=-V_{C}$$\omega _{o}={\sqrt {\frac {1}{T}}}$$T=LC$

## Electromagneticism
### Electric charge

    Charge acquired processElectric chargeCharge quantityElectric fieldMagnetic field Matter + e$^-$--Q-->E<--B ↓ Matter - e$^-$++Q<--E-->B ↑

### Electromagnetic force

    ForceSymbolMathematical formula Electrostatic Force$F_{q}$$K{\frac {q_{+}q_{-}}{r^{2}}}$ Electromotive Force$F_{E}$$qE$ Electromagnetomotive Force$F_{B}$$\pm qvB$ Electromagnetic Force$F_{EB}$$qE\pm qvB=q(E\pm B)$

### Electromagnetic Field

    Configuration Symbol Mathematical Formulas For any configuration$B$$B=LI$ For straight line conductor$B$$B=LI={\frac {\mu }{2\pi r}}I$Circular B field For circular loop conductor$B$$B=LI={\frac {\mu }{2r}}I$Circular B field around a point charge For coil of N circular loops conductor$B$$B=LI={\frac {N\mu }{l}}I$Eleptic B field around the coil

### Electromagnetic Principles

    Electromagnetic field $B$ $LI$ Induced electromagnetic field $\phi$ $-NB=-NLI$ Electromagnetization field $H$ ${\frac {B}{\mu }}={\frac {\phi }{N\mu }}$ Eletromagnetization $\nabla \cdot D=\rho$ $\nabla \times E=-\nabla B$ $\nabla \cdot B=0$ $\nabla \times H=J+\nabla B$
    Coil's voltage induction intencity $V$ $V={\frac {dB}{dt}}=L{\frac {dI}{dt}}$ Turn's induced voltage intencity $\epsilon$ $-{\frac {d\phi }{dt}}=-N{\frac {dB}{dt}}=-NL{\frac {d}{dt}}I$
    Electromagnetic oscillation $\nabla \cdot E=0$ $\nabla \times E={\frac {1}{T}}$ $\nabla \cdot B=0$ $\nabla \times B={\frac {1}{T}}$ Electromagnetic wave $\nabla ^{2}E=-\omega E$ $\nabla ^{2}B=-\omega B$ $E=ASin\omega t$ $B=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f$ $T=\mu \epsilon$ Electromagnetic wave radiation $v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f$ $E=pv=pC=p\lambda f=hf$ $h=p\lambda$ $p={\frac {h}{\lambda }}$ $\lambda ={\frac {h}{p}}={\frac {C}{f}}$

## Photon

Photon is defined as energy of a massless quanta travels as an electromagnetic oscillation wave radiation at speed equal to speed of light Mathematical formula of
    $E=hf=\hbar \omega$
Photon exist in 2 states
    Radiant Photon at threshold frequency fo
       $E=hf_{o}=\hbar \omega _{o}$
    Non Radiant Photon at frequency greater than threshold frequency fo
       $E=hf=\hbar \omega$ . With f>fo
Photon can only exist in one state at a time . This is Heiseinberg's uncertainty principle the success rate of finding photon
    $\Delta p\Delta \lambda ={\frac {1}{2}}{\frac {h}{2\pi }}={\frac {\hbar }{2}}$

### Quanta of Photon

Quantity of photon's energy . Quanta is denoted as h measured in has a constant value h =
    $h=p\lambda$
Quanta process Wave particle duality meaning
    Sometimes it behaves like wave $\lambda ={\frac {h}{p}}$
    Sometimes it behaves like particle $p={\frac {h}{\lambda }}$

### Photon and matter

Photon and matter interacts to create Heat transfer through 3 phases Heat conduction, Heat convection and Heat radiation
    Heat transfer Heat conductionMatter changes it's temperature while absorb heat energy$\Delta T=T_{1}-T_{0}$ $E=mC\Delta T$ Heat convection Matter conducts heat energy to the max at Threshold frequency fo $f_{o}={\frac {C}{f_{o}}}$ $E=hf_{o}$ Heat radiationMatter uses excess energy above maximum absorbing energy to release electron off atom $hf-hf_{o}={\frac {1}{2}}mv^{2}$. When v>0 $v={\sqrt {{\frac {2}{m}}nhf_{o}}}$ with f > f$_o$
Causes matter to decay through 3 kinds of decays
    Mattter decay Reaction Alpha decayUr--> Th - He + Alpha radiation Beta decayC-->N + Beta radiation Gamma decayee) + Gamma radiation
Experiment has shown that, electron of an atom can be freed or binded from absorbing or releasing photon's energy
    Atom decay Absorbing photon energy Releasing photon energy Equilibrium$hf=hf_{o}+{\frac {1}{2}}mv^{2}$$nhf=mvr2\pi$ v${\sqrt {{\frac {2}{m}}(hf-hf_{o})}}={\sqrt {{\frac {2}{m}}(nf_{o})}}$${\frac {1}{2\pi }}{\frac {nhf}{mr}}$ r${\frac {1}{2\pi }}{\frac {nhf}{mv}}$ n$2\pi {\frac {mv}{hf}}$