Formulas


Physics formulas of the above topics. Press the link will take you to the correct position

Mechanics

The quantity, the law, the definitionNotationUnitFormula
Smooth forward motion
distancesms = vt
Steady variable forward motion
accelerationam/s2 a=\frac{v-{v}_{0}}{t}
end speedvm/s v={v}_{0}+at
average speedvkm/s {v}_{k}=\frac{{v}_{0}+v}{2}
positionxm x={x}_{0}+{v}_{0}t+\frac{1}{2}a{t}^{2}
Smooth rotary movement
arc lengthsm s=r\phi
angular velocityωrad/s \omega =\frac{\Delta \phi }{\Delta t}
track speedvm/s v=r\omega
round frequencynl/s n=\frac{1}{T}=\frac{\omega }{2\pi }
Steady variable rotary motion
angular accelerationαrad/s2 \alpha =\frac{\omega -{\omega }_{0}}{t}
final angular velocityωrad/s \omega ={\omega }_{0}+\alpha t
average angular velocityωkrad/s {\omega }_{k}=\frac{{\omega }_{0}+\omega }{2}
angle of rotationφrad \phi ={\phi }_{0}+{\omega }_{0}t+\frac{1}{2}\alpha {t}^{2}
Tangent accelerationatm/s2 {a}_{t}=r\alpha
Normal acceleration
anm/s2 {a}_{n}=\frac{{v}^{2}}{r}
ForceFNF = ma
gravityGG = mg
gravitational forceF=\gamma \frac{{m}_{1}{m}_{2}}{{r}^{2}}
kinetic frictionFμFμ = μN
harmonic forceF = -kx
equation of forward motion
ΣFi = ma
momentumPkgm/sp =mv
impulse of force
INsI = FΔt
WorkWJW = Fss, WF = F * s
PowerPWP=\frac{\Delta W}{\Delta t}, \: P=Fv
Potential energy
EpJ
gravitational fieldEp = mgh
{E}_{p}=-\gamma \frac{mM}{r}
the harmonic force field{E}_{p}=\frac{1}{2}k{x}^{2}
Kinetic energy
EkJ{E}_{k}=\frac{1}{2}m{v}^{2}
Mechanical efficiency
η \eta =\frac{{E}_{a}}{{E}_{0}}=\frac{{P}_{a}}{{P}_{0}}
Harmonic oscillator
position x(t)=A\:sin\:(2\pi ft+\phi )
period of time T=2\pi \sqrt{\frac{m}{k}}
Oscillation period
mathematical pendulum T=2\pi \sqrt{\frac{l}{g}}
physical pendulum T=2\pi \sqrt{\frac{{J}_{A}}{m{r}_{A}g}}
rotational pendulum T=2\pi \sqrt{\frac{J}{D}}
Centre of mass {x}_{0}=\frac{\Sigma {m}_{i}{x}_{i}}{\Sigma {m}_{i}},\: {y}_{0}=\frac{\Sigma {m}_{i}{y}_{i}}{\Sigma {m}_{i}}
Moment of force
MNmM = F⊥r, M = r x F
Equation of rotation
ΣMi = Jα
Angular momentumLkgm2/sL = Jω
Impulse torque Ikgm2/sI = M Δt
The work done by momentum
WJW = M Δφ
Power of rotationPWP = Mω
Rotational energyEkJ{E}_{k}=\frac{1}{2}J{\omega }^{2}
Moments of inertiaJkgm2
figure shafts
object like dot
J = mr2
closed cylinder
J=\frac{1}{2}m{r}^{2}
thin-walled ring
J = mr2
thick-walled ring
J=\frac{1}{2}m({{r}_{1}}^{2}+{{r}_{2}}^{2})
thin rod
J=\frac{1}{3}m{l}^{2}
J=\frac{1}{12}m{l}^{2}
rectangular plate
J=\frac{1}{12}m({a}^{2}+{b}^{2}) 
solid ball
J=\frac{2}{5}m{r}^{2}
thin-walled ball
J=\frac{2}{3}m{r}^{2}
Steiner’s rule
JA = Jp + ma2
TensionσN/m2\sigma =\frac{F}{A}
Hooke’s law of elasticityEN/m2\frac{F}{A}=E\frac{\Delta l}{l}
Densityρkg/m3\rho =\frac{m}{V}
PressurepPap=\frac{F}{A}
Hydrostatic pressure
pPap = hρg
Buyoancy forceNNN = ρVg
Surface tension
forceFNF = σl
energyEJE = σA
Viscosity
forceFNF=\frac{\eta Av}{d}
Bernoulli’s equation
{p}_{0}+\frac{1}{2}\rho {v}^{2}+h\rho g=vakio

 

Thermodynamics

Quantity, law, definitionQuantityUnitFormula
Thermodynamic temperature TK T=\frac{2}{3k}{\bar{E}}_{k},\: k=\frac{R}{{N}_{A}}
Temperature rangeK \frac{T}{K}=\frac{t}{^{\circ} C}+273,15
t°C \frac{t}{^{\circ} C}=\frac{T}{K}-273,15
°C \frac{t}{^{\circ} C}=\frac{5}{9}\left(\frac{t}{^{\circ} F}-32 \right)
°F \frac{t}{^{\circ} F}=\frac{9}{5}\frac{t}{^{\circ} C}+32
Dalton’s law (partial pressure)
 p=\Sigma {p}_{i}
General equation of gases \frac{pV}{T}=vakio, \: pV=nRT
Poisson’s law
adiabatic change p{V}^{\kappa }=vakio,\: \kappa =\frac{{c}_{p}}{{c}_{v}}
Heat expansion
lengthα1/°C l={l}_{0}(1+\alpha \Delta t)
volumeγ1/°C V={V}_{0}(1+\gamma \Delta t)
Compressibilityκ1/Pa V={V}_{0}(1-\kappa \Delta p)
Thermodynamic system
total energy E=U+{E}_{p}+{E}_{k}
first basic rule \Delta U=Q+W
internal energy of ideal gasUJ U=\frac{3}{2}nRT
Heat capacity
CJ/K C=cm
Heat energyQJ Q=cm\Delta t
Melting Q=sm
Evaporation Q=sr
Heat conduction
λ Q=\lambda \frac{A\Delta \upsilon }{d}t
EntropySJ/K \Delta S=\frac{\Delta Q}{T}
Heat engine
efficiencyη \eta =\frac{{Q}_{1}-{Q}_{2}}{{Q}_{1}}
ideaal efficiency {\eta }_{max} =\frac{{T}_{1}-{T}_{2}}{{T}_{1}}
Cooling machine
performanceε \epsilon =\frac{{Q}_{2}}{{Q}_{1}-{Q}_{2}}=\frac{1}{\eta }-1
ideal performance {\epsilon }_{max}=\frac{{T}_{2}}{{T}_{1}-{T}_{2}}=\frac{1}{{\eta }_{max} }-1
Heat pump
performanceε \epsilon=\frac{{Q}_{1}}{{Q}_{1}-{Q}_{2}}=\frac{1}{\eta }
ideal performance {\epsilon }_{max}=\frac{{T}_{1}}{{T}_{1}-{T}_{2}}=\frac{1}{{\eta }_{max} }

 

Wave motion and optics

Quantity, law, the numberSymbolUnitFormula
Fundamental equation of wave motion
 v=f\lambda
IntesityIW/m2 I=\frac{P}{A}
Energy density
wJ/m3 w=k{f}^{2}{A}^{2}, \: w=\frac{I}{v}
Doppler effect
wave source moves f={f}_{0}\frac{c}{c\pm v}
observer moves f={f}_{0}\frac{c\pm v}{c}
Speed of sound in the gas
c \frac{{c}_{1}}{{c}_{2}}=\sqrt{\frac{{T}_{1}}{{T}_{2}}}
Sound intensity level
LdB L=10\: lg\frac{I}{{I}_{0}}dB,\: {I}_{0}=1\: pW/{m}^{2}
Refraction \frac{sin\:{\alpha }_{1}}{sin\:{\alpha }_{2}}=\frac{{v}_{1}}{{v}_{2}}=\frac{{n}_{2}}{{n}_{1}}={n}_{12}
Brewster’s law tan\: {\alpha }_{B}=\frac{{n}_{2}}{{n}_{1}}
Lattice equation (diffraction) d\: sin\: \alpha =k\lambda
Projection equation \frac{1}{a}+\frac{1}{b}=\frac{1}{f}
folding strength
Dl/m =d D=\frac{1}{f}
Line magnificationm m=\left|\frac{b}{a} \right|
Angle magnificationM M=\frac{tan\:{\alpha }_{2}}{tan\:{\alpha }_{1}}
Magnifications
magnifying glass M=\frac{s}{f}
microscope M=\frac{Ls}{{f}_{0b}{f}_{0k}}
telescope M=\frac{{f}_{ob}}{{f}_{ok}}
BrightnessIcd I=\frac{\Phi }{\omega }
LuminanceLcd/m2 L=\frac{I}{A}
Luminous fluxΦlm \Phi =I\omega
Light intensityElx E=\frac{\Phi }{A}
Lambert’s law
 I={I}_{0}\:cos\:\alpha
Distance law E=\frac{{I}_{0}\:cos\:\alpha }{{r}^{2}}

 

Electricity and magnetism

Quantity, law, definitionSymbolUnitFormula
Columbs force in the vacuum
FN F=\frac{1}{4\pi {\varepsilon }_{0}}\frac{{Q}_{1}{Q}_{2}}{{r}^{2}}
charge  coveringσC/m2 \sigma =\frac{Q}{A}
Electric field
strengthEN/C, V/m E =\frac{F}{Q}
potentialVV V=\frac{{E}_{p}}{Q}
Voltage (potential difference)UV {U}_{BA}={V}_{B}-{V}_{A}=\frac{{W}_{AB}}{Q}
homogenous electric field U=Ed
Point charge electric field
strengthEN/C, V/m E=\frac{1}{4\pi {\varepsilon }_{0}}\frac{Q}{{r}^{2}}
potentialVV V=\frac{1}{4\pi {\varepsilon }_{0}}\frac{Q}{r}
Relative permittiivityεr {\varepsilon }_{r}=\frac{{E}_{0}}{E}=\frac{\varepsilon }{{\varepsilon }_{0}}
Capacitor
capacitanceCF C=\frac{Q}{U}
plate capacitor C={\varepsilon }_{0}{\varepsilon }_{r}\frac{A}{d}
energyEJ E=\frac{1}{2}C{U}^{2}
Capacitors
in series \frac{1}{C}=\sum \frac{1}{{C}_{i}}
in parallel C=\sum {C}_{i}
ResistanceR\Omega R=\frac{U}{I}
Conductor R=\rho \frac{l}{A}
Resistivity\rho\Omega m\rho ={\rho }_{0}(1+\alpha \Delta t)
Resistors
in series R=\sum {R}_{i}
in parallel \frac{1}{R}=\sum \frac{1}{{R}_{i}}
Electric currentIA I=\frac{\Delta Q}{\Delta t}
Electrical energyEJ E=UIt
Electrical powerPW P=UI
Parallel conductors
FN F=\frac{{\mu }_{0}}{2\pi }\frac{{I}_{1}{I}_{2}}{r}l
Magneetic flux density
BT
Biot and Sawart law \Delta B=\frac{{\mu }_{0}}{4\pi }\frac{I\Delta l}{{r}^{2}}sin\:\alpha
 direct conductor B=\frac{{\mu }_{0}}{2\pi r}I
circular conductor, at the center B=\frac{{\mu }_{0}}{2r}I
Long coil, inside B=N\frac{{\mu }_{0}}{l}I
toroid, inside B=N\frac{{\mu }_{0}}{2\pi r}I
Relative permeability
μr {\mu }_{r}=\frac{B}{{B}_{0}}=\frac{\mu }{{\mu }_{0}}
Magnetic field strength
HA/m H=\frac{B}{{\mu }_{0}}
In the magnetic field
charged particle F=Q\:v\:B\:sin\:\alpha ,\: F=Qv\:x\:B
direct conductor F=I\:l\:B\:sin\:\alpha
coilMNm M=N\:I\:AB\:sin\:\alpha
Magneetic flux
ΦWb \Phi =AB\:cos\:\phi =A\cdot B
Induction voltage
eV
straight wire e=l\:v\:B\:sin\:\alpha
coil e=-N\frac{\Delta \Phi }{\Delta t}
self induction e=-L\frac{\Delta I}{\Delta t}
InductanceLH L=N\frac{\Phi}{I}
long coil L={\mu }_{0}\frac{{N}^{2}A}{l}
Magneetic field energy
EJ E=\frac{1}{2}L{I}^{2}
Sinusoidal alternative voltage
uV u=\hat{u}\:sin\:2\pi ft
effective voltage {U}_{eff}=U=\frac{\hat{u}}{\sqrt{2}}
effective current {I}_{eff}=I=\frac{\hat{i}}{\sqrt{2}}
power P=UI\:cos\:\phi
ReactanceXΩ
inductiveXL {X}_{L}=\omega L=2\pi fL
capacitiveXC {X}_{C}=\frac{1}{\omega C}=\frac{1}{2\pi fC}
RLC-cirvuit
voltageuV u=\hat{u}\:sin\:2\pi ft
currentiA i=\hat{i}\:sin\:(2\pi ft-\phi )
impedanceZΩ Z=\sqrt{{R}^{2}+{({X}_{L}-{X}_{C})}^{2}}
phase differenceφ tan\:\phi=\frac{{X}_{L}-{X}_{C}}{R}
Transformer \frac{{N}_{1}}{{N}_{2}}=\frac{{U}_{1}}{{U}_{2}}\approx \frac{{I}_{1}}{{I}_{2}}
Oscillator frequency (resonance frequency)
fHz {f}_{0}=\frac{1}{2\pi \sqrt{LC}}
Speed of the electromagnetic wave motion in the vacuumcm/s c=\frac{1}{\sqrt{{\varepsilon }_{0}{\mu }_{0}}}

 

Radiation-, atomic- and nuclear physics

Quantity, law, definitionSymbolUnitFormula
Stefanja Boltzman law I=\sigma {T}^{4}
Wien’s displacement law
 T{\lambda }_{maks}=b
The radiation quantum
energy E=hf
momentum p=\frac{h}{\lambda }=\frac{E}{c}
Compton effect
 \Delta \lambda =\frac{h}{{m}_{e}c}(1-cos\:\theta)
Weakening law I={I}_{0}{e}^{-\mu x}
de Brogel waves
λ \lambda =\frac{h}{mv}
Uncertainty principle \Delta x\Delta p\geq \frac{1}{2}h,\: \Delta E\Delta t\geq \frac{1}{2}h, \:h=\frac{h}{2\pi }
Bragg’s law
 2d\:sin\:\theta =k\lambda
quantum numbers
principal quantum numbern n=1,\:2,\:3,\:...
azimuthal quantum numberl l=0,\:1,\:2,\:...,\:n-1
magneetic quantum numberm {m}_{l}=0,\:\pm 1,\:\pm 2,\:...,\:\pm l
spin quantum numbers s=\pm \frac{1}{2}
Bohr hydrogen atom model
quantum clause mvr=n\cdot \frac{h}{2\pi }
the total energy {E}_{n}=-\frac{m{e}^{4}}{8\varepsilon _{0}^{2}{h}^{2}}\cdot \frac{1}{{n}^{2}}
radius of the track {r}_{n}=\frac{{\varepsilon }_{0}{h}^{2}}{\pi {e}^{2}{m}_{e}}\cdot {n}^{2}
speed {r}_{n}=\frac{{e}^{2}}{2{\varepsilon }_{0}h}\cdot \frac{1}{n}
wavelength \frac{1}{\lambda }={R}_{H}\left(\frac{1}{{m}^{2}}-\frac{1}{{n}^{2}} \right)
The radius of the core
 r=1,4\cdot \sqrt[3]{A}\:fm\:\:\:\:\:\:A=Z+N
Bond partbeV/nukl. b=\frac{{E}_{B}}{A}=\frac{\Delta m{c}^{2}}{A}
Fission law N={N}_{0}{e}^{-\lambda t}
ActivityABq A=\lambda N={A}_{0}{e}^{-\lambda t}
Radioactive constant, half-lifeT1/2 {T}_{1/2}=\frac{ln\:2}{\lambda }
Median lifetimeτ \tau =\frac{1}{\lambda }
Equivalent portion
HSv H=Q\cdot D

 

Theory of relativity

Quantity, law, definitionFormula
Combining speed
 v=\frac{{v}_{1}+{v}_{2}}{1+\frac{{v}_{1}{v}_{2}}{{c}^{2}}}
Lorentz contraction
 l={l}_{0}\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}
Time dilation t=\frac{{t}_{0}}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}
Mass depending the speed m=\frac{{m}_{0}}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}
Kinetic energy {E}_{k}=m{c}^{2}-{m}_{0}{c}^{2}
The total energy E=m{c}^{2}=c\sqrt{{p}^{2}+{({m}_{0}c)}^{2}}