Laws¶
A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior.
Contents:
- Astronomy
- Astronomy (Relativistic)
- Absolute magnitude of stars from apparent magnitude and distance
- Approximate lifetime of stars located on the main sequence
- Change in apparent magnitude from distance
- Latitude from zenith angle and declination
- Lifetime of star on main sequence
- Luminosity of star from absolute magnitude
- Luminosity of Sun in future from luminosity in present
- Luminosity of Sun in past from luminosity in present
- Object’s angular altitude in upper culmination
- Radius of planetary orbits from number
- Ratio of luminosities from ratio of masses of stars
- Speed of galaxy from distance to galaxy
- Chemistry
- Electrochemistry
- Potential energy models
- Avogadro constant is particle count over amount of substance
- Boundary of thermalization zone of atomized atoms in magnetron
- Coefficient of volumetric ionization of neutral molecules by electrons
- Cross section of interaction in Coulomb’s interaction model
- Cross section of interaction in elastic interaction model
- Cross section of interaction in model of hard spheres
- Cross section of interaction in recharge model
- Cross section of ionization of atom by electrons per Granovsky
- Cross section of ionization of atom by electrons per Lotz-Drevin
- Distance of greatest convergence of particles in magnetron
- Electron distribution function in gas plasma per Druyvestein
- Electron distribution function in gas plasma per Maxwell
- Electron current in probe circuit in gas plasma
- Energy transfer coefficient for elastic scattering in magnetron
- Etching rate of target in magnetron
- Mean free path of particles in gaseous medium
- Mass of film deposited during electrolysis
- Molar mass via molecular mass
- Number density via volumetric density and molar mass
- Number of collisions of particle with gas in magnetron
- Reaction equilibrium constant via standard Gibbs energy
- Speed of charged particles in gas via mobility
- Condensed matter
- Concentration of intrinsic charge carriers
- Current density from mobility
- Current density in thermionic emission per Richardson
- Current density via number density and drift velocity
- Diffusion coefficient from energy and temperature
- Drift velocity of charge carriers
- Effective mass of electron via energy
- Equilibrium voltage difference in p-n junction via concentrations
- Resistance from temperature
- Conservation
- Abbe invariant of two optical environments is constant
- Charge is constant
- Initial mass equals final mass
- Mass is constant
- Initial mechanical energy equals final mechanical energy
- Mechanical energy is constant
- Mixture mass equals sum of component masses
- Amount of mixture is sum of amounts of components
- Initial momentum equals final momentum
- Momentum is constant
- Dynamics
- Damped oscillations (Dynamics)
- Deformation (Dynamics)
- Bulk modulus via Young modulus and Poisson ratio
- Elastic energy density of bulk compression via pressure
- Elastic energy density of compression via strain
- Engineering normal strain is total deformation over initial dimension
- Poisson ratio is transverse to axial strain ratio
- Pressure is Maclaurin series of strain
- Rotational stiffness is torque applied over angle
- Superposition of small deformations
- Tensile stress is Young’s modulus times strain
- Fields (Dynamics)
- Springs
- Dynamics (Vector)
- Acceleration is force over mass
- Braking path via speed and friction force
- Buoyant force from density and volume
- Coefficient of stiffness from area and length
- Displacement in forced non-resonant oscillations
- Force is derivative of momentum
- Forced oscillations equation
- Friction force from normal force
- Instantaneous power is force times speed
- Kinetic energy from mass and speed
- Kinetic energy from rotational inertia and angular speed
- Kinetic energy via momentum
- Maximum height from initial speed
- Mechanical work is force times distance
- Momentum derivative of kinetic energy is speed
- Period of ideal pendulum from length
- Period of physical pendulum
- Period of spring from mass
- Period of torsion pendulum from rotational inertia
- Elastic potential energy from displacement
- Potential energy from mass and height
- Pressure from force and area
- Reaction force equals action force
- Reduced mass of a two-body system
- Displacement in resonant oscillations
- Rocket thrust is rocket mass times acceleration
- Rotational work is torque times angular distance
- Rocket speed from mass and impulse
- Torque via force and radial distance
- Torque via rotational inertia and angular acceleration
- Total work is change in kinetic energy
- Work is integral of force over distance
- Electromagnetism
- Circuits
- Couplers
- Attenuation of three link microwave attenuator
- Admittance of rectangular loop coupler
- Total gain of transistor amplifier
- Impedance of Wilkinson microstrip divider
- Section length of multistage transformer
- Relative operating bandwidth of quarter-wave transformer
- Resistor resistance in Wilkinson divider
- Transient attenuation of separate loop coupler with cascade connection
- Wave impedance of even mode of Lange coupler
- Wave impedance of odd mode of Lange coupler
- Wave impedance of Lange coupler
- Diodes
- Current from voltage and diode constant in vacuum diode
- Current from voltage and triode constant in vacuum triode
- Diode constant for parallel-plane vacuum diode
- Diode constant of cylindrical diode
- Direct permeability coefficient of triode with flat electrodes
- Internal resistance of vacuum diode
- Limit operating frequency of vacuum diode
- Charge density in diode
- Steepness of volt-ampere characteristic of vacuum diode
- Voltage of equivalent diode for pentode
- Equivalent diode voltage for tetrode
- Equivalent diode voltage for triode
- Filters
- Transmission coefficient approximation of low-pass filter
- Band pass Chebyshev filter order from distortion and frequency
- Butterworth filter order from distortion and frequency
- Filter order from distortion and frequency
- High pass Chebyshev filter from distortion and frequency
- Low-pass Chebyshev filter order from distortion and frequencies
- Resonators
- Coupling parameter of resonator from quality factor
- Coupling parameter of resonator from resistance
- Instantaneous energy of resonator
- Quality factor of loaded resonator from circuit parameters
- Quality resonator of loaded resonator from quality factors
- Quality factor of resonator
- Quality factor of empty rectangular resonator for traverse electric waves
- Quality factor of filled rectangular resonator
- Resonant frequency of rectangular resonator
- Resonant frequency of ring resonator
- Transmission lines
- Coplanar lines
- Microstrip lines
- Standing wave ratio from reflection coefficient
- Standing wave ratio from voltage
- Hybrid parameters matrix equation
- Impedances of π-type circuit of transmission line
- Impedances of T-type circuit of transmission line
- Input impedance from transmission matrix
- Input impedance of lossless transmission line
- Input impedance of lossy transmission line
- Reflection coefficient from ratio of average power to incident power
- Standing wave ratio from ratio of average power to incident power
- Reflection coefficient from load and surge impedance
- Scattering matrix equation
- Scattering matrix to transmission matrix
- Admittance matrix equation
- Impedance matrix equation
- Transmission matrix equation
- Transmission matrix for parallel load in line
- Transmission matrix for serial load in line
- Transmission matrix of lossless transmission line
- Transmission matrix of lossy transmission line
- Transmission matrix of π-type matrix
- Transmission matrix of T-type circuit
- Surge impedance of microstrip line when effective width is greater than substrate thickness
- Surge impedance of microstrip line when effective width is less than substrate thickness
- Waveguides
- Attenuation coefficient in dielectric
- Attenuation coefficient in dielectric in rectangular waveguide
- Attenuation coefficient in metal
- Attenuation coefficient in metal in rectangular waveguide for transverse electric waves
- Attenuation coefficient in metal in rectangular waveguide for transverse magnetic waves
- Wave impedance in rectangular waveguide for transverse electric waves
- Characteristic resitance of rectangular waveguide for transverse magnetic waves
- Critical wavelength in rectangular waveguide
- Group speed of wave in rectangular waveguide
- Maximum electric field strength of main wave in rectangular waveguide
- Maximum voltage in coaxial line
- Phase speed of wave in rectangular waveguide
- Power carried by coaxial waveguide
- Power carried by main wave of rectangular waveguide
- Specific capacitance of coaxial waveguide
- Specific conductivity of coaxial waveguide
- Specific inductance of coaxial waveguide
- Specific resistance of coaxial waveguide
- Surface resistance of metal
- Wave resistance of coaxial waveguide
- Wavelength in rectangular waveguide
- Admittance in parallel connection
- Capacitance in parallel connection
- Capacitance is proportional to plate area
- Capacitance of spherical capacitor
- Capacitor impedance from capacitance and frequency
- Capacitor impedance from capacitor reactance
- Coil impedance from inductive reactance
- Coil impedance via inductance and frequency
- Energy stored in capacitor via capacitance and voltage
- Energy stored in inductor via inductance and current
- Impedance in serial connection
- Impedance module of serial resistor-coil-capacitor circuit
- Inductance in serial connection
- Input impedance of thin film resistor
- Oscillation period of inductor-capacitor network
- Resistivity of serial resistors
- Sum of currents through junction is zero
- Sum of voltages in loop is zero
- Time constant of resistor-capacitor circuit
- Capacitance of p-n varactor junction
- Voltage across charging capacitor in serial resistor-capacitor circuit
- Couplers
- Maxwell equations
- Electromagnetism (Vector)
- Absolute permittivity via relative permittivity
- Admittance is conductance and susceptance
- Capacitance from charge and voltage
- Wave impedance from permeability and permittivity
- Charge is quantized
- Corona discharge current from voltage
- Current is voltage over resistance
- Electric charge is constant in isolated system
- Electric dipole moment is charge times distance
- Electric displacement is permittivity times electric field
- Electric field due to dipole
- Electric field due to point charge
- Electric field is force over test charge
- Electric field of uniformly charged plane
- Electric field outside charged sphere
- Electric flux through closed surface via total charge
- Electric field in gas gap between two electrodes
- Electromotive force induced in moving contour
- Electromotive force induced in rotating rod
- Electromotive force induced in rotating coil
- Electrostatic force via charges and distance
- Electrostatic potential due to point charge
- Electrostatic potential energy of two charges via distance
- Electrostatic potential is work to bring from reference point over charge
- Energy density via permittivity and electric field
- Energy of magnetic field of coil
- Energy via constant power and time
- Force between parallel wires
- Inductance is magnetic flux over current
- Inductance is proportional to turn count
- Inductance via number of turns and coil volume
- Instantaneous energy of electric field
- Magnetic field due to infinite wire
- Magnetic field of coil
- Magnetic flux from magnetic flux density and area
- Magnetic flux density from magnetic field strength
- Magnetic flux density of linear conductor of finite length
- Magnetic moment via current and contour area
- Period of rotation of charged particle in magnetic field
- Power factor is real power over apparent power
- Power via current and resistance
- Power via voltage and current
- Power via voltage and resistance
- Radius of curvature of charged particle in magnetic field
- Resistance via resistivity and dimensions
- Self-induced electromotive force via time derivative of current
- Voltage is electric field times distance
- Voltage is line integral of electric field
- Circuits
- Fields
- Geometry
- Gravity
- Radial motion
- Average potential energy via average kinetic energy
- Potential energy of radial planetary motion
- Radial kinetic energy plus potential energy is constant
- Semimajor axis via Kepler’s constant and total energy
- Semiminor axis of elliptical orbit via orbit parameters
- Total energy is negative average kinetic energy
- Gravity (Vector)
- Angle of rotation during gravitational maneuver
- Area rate of change is proportional to angular momentum
- Corrected planet period squared is proportional to cube of semimajor axis
- Easterly deviation from plumbline of falling bodies
- Eccentricity of orbit
- First escape speed
- Free fall acceleration from height
- Gravitational potential energy
- Gravitational radius of massive body
- Gravitational force from mass and distance
- Kepler’s constant via attracting body mass
- Semimajor axis of orbit via mass and speed
- Maximum angle of rotation during gravitational maneuver
- Maximum height of body thrown at angle to horizon
- Time of flight of a projectile via initial velocity
- Time of flight of a projectile via maximum height
- Orbital speed from semimajor axis and planet mass
- Planet period squared is proportional to cube of semimajor axis
- Radius of geostationary orbit
- Horizontal displacement of projectile
- Second escape velocity
- Southerly deviation from plumbline of falling bodies
- Third cosmic speed from orbital and second cosmic speed
- Radial motion
- Fluid mechanics
- Dynamic pressure from speed
- Efficiency of hydraulic press from force and height
- Efflux speed via height
- Efflux speed via pressure and density
- Excess pressure under curved surface of bubble
- Froude number formula
- Pressure difference at pipe ends from dynamic viscosity and flow rate
- Hydraulic stress is bulk modulus times strain
- Hydrostatic pressure from density, height and acceleration
- Hydrostatic pressure via density and height
- Inner pressure is constant
- Inner pressure is sum of pressures
- Force to area ratio in hydraulic press
- Capillary rise from surface tension and contact angle
- Mach number is flow speed over speed of sound
- Nusselt number formula
- Pressure of liquid in vessel moving horizontally
- Pressure of liquid in vessel moving vertically
- Reynolds number formula
- Shear stress is proportional to speed gradient
- Submerged volume of floating body via density ratio
- Surface tension force via surface tension and length
- Volume flux is constant
- Weight in fluid via ratio of densities
- Kinematics
- Damped oscillations (Kinematics)
- Rotational inertia (Kinematics)
- Kinematics (Vector)
- Absolute velocity of arbitrary motion
- Acceleration due to non-uniform rotation
- Acceleration is normal plus tangential acceleration
- Acceleration of transfer between relative frames
- Center of mass for a system of particles
- Centrifugal acceleration via centripetal acceleration
- Centripetal acceleration via cross product
- Centripetal acceleration via vector rejection
- Coriolis acceleration
- Linear displacement is angular displacement cross radius
- Velocity relative to reference frame
- Angular momentum is rotational inertia times angular speed
- Angular position is arc length over radius
- Angular position via constant angular acceleration and time
- Angular position via constant angular speed and time
- Angular speed via constant angular acceleration and time
- Average angular speed is angular distance over time
- Centripetal acceleration via angular speed and radius
- Centripetal acceleration via linear speed and radius
- Classical addition of velocities
- Displacement in simple harmonic motion
- Position via constant acceleration and time
- Position via constant speed and time
- Speed via angular speed and radius
- Speed via constant acceleration and time
- Tangential acceleration via angular acceleration and radius
- Nuclear physics
- Buckling (Nuclear physics)
- Geometric buckling for uniform cylinder
- Geometric buckling for uniform parallelepiped
- Geometric buckling for uniform slab
- Geometric buckling for uniform sphere
- Geometric buckling from multiplication factors and diffusion area
- Geometric buckling from macroscopic cross sections and diffusion coefficient
- Geometric buckling from neutron flux
- Material buckling from material cross sections and diffusion coefficient
- Neutron flux for uniform cylinder
- Neutron flux for uniform parallelepiped
- Neutron flux for uniform slab
- Neutron flux for uniform sphere
- Diffusion area from diffusion coefficient and absorption cross section
- Diffusion equation from neutron flux
- Effective multiplication factor from infinite multiplication factor and probabilities
- Fast fission factor from resonance escape probability
- Fast non-leakage probability from Fermi age and geometric buckling
- Infinite multiplication factor formula
- Infinite multiplication factor from macroscopic cross sections
- Solution to the exponential decay equation
- Macroscopic cross section from mean free path
- Macroscopic cross section from microscopic cross section and number density
- Macroscopic transport cross section from macroscopic scattering cross section
- Migration area from diffusion length and Fermi age
- Average cosine of scattering angle from mass number
- Diffusion coefficient from macroscopic scattering cross section
- Reproduction factor from macroscopic cross sections in fuel
- Resonance escape probability from resonance absorption integral
- Thermal non-leakage probability from diffusion area and geometric buckling
- Thermal utilization factor from macroscopic absorption cross sections
- Buckling (Nuclear physics)
- Optics
- Angle of light deflection in prism
- Bragg diffraction from angle of diffraction and wavelength
- Film thickness for minimum interference
- Focal length of a concave spherical mirror
- Interference due to two slits
- Interference maximum
- Interference minimum
- Irradiance of light after polarizer
- Lens focus from object and image
- Light pressure
- Linear magnification from distance to object and distance to image
- Linear magnification from object height and image height
- Optical distance difference from optical distances
- Optical path length from geometrical path length and refractive index
- Optical power from focus distance
- Optical power from thin lens radii and refractive indices
- Optical power of spherical lens from refractive indices and distances
- Radiation intensity from energy, area, and time
- Radius of dark Newton’s ring formula
- Refraction angle from enviroments
- Resolution of telescope
- Quantities
- Quantum mechanics
- Harmonic oscillator (Quantum mechanics)
- Schrödinger equation
- Expectation value of observable
- Probability density of quantum state
- Relativistic
- Relativistic (Vector)
- Coordinate conversion at constant velocity
- Lorentz transformation of time
- Proper time for timelike intervals
- Relativistic kinetic energy
- Relativistic length via rest length and speed
- Relativistic mass via rest mass and speed
- Relativistic momentum via rest mass and speed
- Relativistic sum of velocities
- Relativistic time dilation
- Spacetime interval via time and distance
- Spacetime interval is Lorentz invariant
- Total energy via momentum and rest mass
- Total energy via relativistic mass
- Thermodynamics
- Bose—Einstein statistics
- Dielectric Thermodynamics
- Enthalpy change via entropy change and electric field change
- Enthalpy of dielectrics
- Free energy change via temperature change and electric displacement change
- Gibbs energy change via temperature change and electric displacement change
- Gibbs energy of dielectrics
- Internal energy change via heat and electric displacement change
- Equations of state
- Euler relations
- Fermi—Dirac statistics
- Heat transfer
- Maxwell—Boltzmann statistics
- Relativistic Thermodynamics
- Average kinetic energy of ideal gas from temperature
- Average speed in Maxwell—Boltzmann statistics
- Average square speed in Maxwell—Boltzmann statistics
- Canonical partition function of a classical discrete system
- Change in entropy of ideal gas from volume and temperature
- Chemical potential is Gibbs energy per particle
- Chemical potential is particle count derivative of enthalpy
- Chemical potential is particle count derivative of free energy
- Chemical potential is particle count derivative of Gibbs energy
- Chemical potential is particle count derivative of internal energy
- Chemical potential of ideal gas
- Classical isochoric molar heat capacity of solids
- Compressibility factor via intermolecular force potential
- Diffusion coefficient of spherical Brownian particles from temperature and dynamic viscosity
- Diffusion flux from diffusion coefficient and concentration gradient
- Dynamic viscosity of gas from temperature
- Efficiency of heat engine
- Enthalpy derivative via volume derivative
- Enthalpy differential
- Enthalpy is internal energy plus pressure energy
- Enthalpy via Gibbs energy
- Entropy change in reversible process
- Entropy derivative via volume derivative
- Entropy from statistical weight
- Entropy is derivative of free energy
- Entropy is derivative of Gibbs energy
- Entropy of independent subsystems is sum of their entropies
- Fractional volume change via small temperature change
- Free energy differential
- Gas mixture pressure from partial pressures
- Gas pressure change from temperature
- Gibbs energy differential
- Gibbs energy via enthalpy
- Grashof number
- Heat is heat capacity times temperature change
- Heat of combustion via mass
- Heat of vaporization via mass
- Helmholtz free energy via internal energy
- Infinitesimal work in quasistatic process
- Intensive parameters relation
- Internal energy change of ideal gas via temperature
- Internal energy change via heat and work
- Internal energy differential
- Internal energy of ideal gas via temperature
- Internal energy via Helmholtz free energy
- Isentropic speed of sound
- Isobaric molar heat capacity of ideal gas via adiabatic index
- Isobaric potential from heat capacity
- Isobaric potential of temperature dependent heat capacity
- Isochoric and isobaric heat capacities of homogeneous substance
- Isochoric and isobaric heat capacities of ideal gas
- Isochoric molar heat capacity of ideal gas via adiabatic index
- Isochoric molar heat capacity of ideal gas via degrees of freedom
- Laplace pressure of spherical shapes
- Latent heat of fusion via mass
- Mean free path of random motion
- Number of impacts on the wall from area and speed
- Prandtl number via dynamic viscosity and thermal conductivity
- Pressure and temperature in isochoric process
- Adiabatic process equation via pressure and volume
- Pressure and volume in isothermal process
- Pressure from number density and kinetic energy
- Pressure of ideal gas from height and temperature
- Probability of finding ideal gas molecules in volume
- Probability of ideal gas macrostate
- Quantum isochoric molar heat capacity of solids
- Radiance of black body from temperature
- Radiation power via temperature
- Rate of energy conduction through slab
- Relative humidity is ratio of vapor pressure
- Speed of sound in ideal gas
- Temperature derivative via volume derivative
- Temperature is derivative of internal energy
- Total energy transfer is zero in adiabatically isolated system
- Total particle count is sum of occupancies
- Volume and temperature in isobaric process
- Volumetric and linear expansion coefficients in isotropic materials
- Volumetric expansion coefficient of ideal gas
- Work is integral of pressure over volume
- Work of ideal gas in isobaric process
- Work of ideal gas in isothermal process
- Waves
- Blackbody radiation
- Waves (Relativistic)
- Waves (Vector)
- Average power of sinusoidal wave on stretched string
- Displacement in interfering waves
- Displacement in standing wave
- Frequency of electron transition in Hydrogen
- Frequency shift from speed in arbitrary motion
- Frequency shift from speed in collinear motion
- Fully constructive interference condition
- Fully destructive interference condition
- Group velocity from dispersion relation
- Intensity of sound wave via displacement amplitude
- Light frequency change is proportional to gravitational potential change
- Peak wavelength via temperature
- Phase of traveling wave
- Phase shift between two points
- Phase speed of wave on stretched string
- Phase speed from angular frequency and wavenumber
- Photoelectron energy from photon energy
- Photon energy is proportional to angular frequency
- Photon energy is proportional to linear frequency
- Photon momentum is proportional to angular wavenumber
- Photon momentum is proportional to energy
- Position of antinodes in standing wave
- Position of nodes in standing wave
- Pressure amplitude in sound wave
- Refractive index via permittivity and permeability
- Resonant frequencies of stretched string with fixed ends
- Sine of Mach cone angle via Mach number
- Speed of light via vacuum permittivity and permeability
- Speed of sound via bulk modulus and density
- General solution to wave equation in one dimension
- Wavelength from phase speed and period
- Wavelength of standing wave in string with fixed ends
- Wave speed from medium permittivity and permeability
- Wave speed from medium