Symplyphysics¶
Physics laws implemented as code. Based on SymPy Python library.
Autogenerated from Symplyphysics project.
Contents:
- Laws
- Astronomy
- Astronomy (Relativistic)
- Absolute magnitude of stars from apparent magnitude and distance
- Angle of rotation during gravitational maneuver
- Approximate lifetime of stars located on the main sequence
- Change in apparent magnitude from distance
- Eccentricity of orbit
- Semimajor axis of orbit via mass and speed
- 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
- Maximum angle of rotation during gravitational maneuver
- Object’s angular altitude in upper culmination
- Orbital speed from semimajor axis and planet mass
- Radius of geostationary orbit
- Radius of planetary orbits from number
- Ratio of luminosities from ratio of masses of stars
- Resolution of telescope
- Speed of galaxy from distance to galaxy
- Rocket speed from mass and impulse
- Third cosmic speed from orbital and second cosmic speed
- 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
- Molar mass via molecular mass
- Number density via volumetric density and molar mass
- Reaction equilibrium constant via standard Gibbs energy
- Condensed matter
- Conservation
- 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
- 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
- Diodes
- Filters
- Resonators
- Transmission lines
- Waveguides
- Admittance in parallel connection
- Capacitance in parallel connection
- Capacitance is proportional to plate area
- Capacitance of spherical capacitor
- Capacitor impedance from capacitance and frequency
- 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
- Inductance in serial connection
- 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
- Voltage across charging capacitor in serial resistor-capacitor circuit
- Maxwell equations
- Electromagnetism (Vector)
- Absolute permittivity via relative permittivity
- Admittance is conductance and susceptance
- Capacitance from charge and voltage
- Charge is quantized
- 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
- 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 via constant power and time
- Inductance is magnetic flux over current
- Inductance via number of turns and coil volume
- Magnetic field due to infinite wire
- Magnetic field of coil
- 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)
- 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
- 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
- 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
- Planet period squared is proportional to cube of semimajor axis
- Horizontal displacement of projectile
- Second escape velocity
- Southerly deviation from plumbline of falling bodies
- Radial motion
- Fluid mechanics
- Dynamic pressure from speed
- Efflux speed via height
- Efflux speed via pressure and density
- Hydraulic stress is bulk modulus times strain
- Hydrostatic pressure via density and height
- Inner pressure is constant
- Inner pressure is sum of pressures
- Mach number is flow speed over speed of sound
- 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
- 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 indeces
- 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
- Quantities
- Quantum mechanics
- 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
- 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
- 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
- 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
- Astronomy
- Definitions
- Definitions (Vector)
- Acceleration is speed derivative
- Admittance is inverse impedance
- Angular acceleration is angular speed derivative
- Angular speed is angular distance derivative
- Angular wavenumber is inverse wavelength
- Boltzmann factor via state energy and temperature
- Compliance is inverse stiffness
- Compressibility factor is deviation from ideal gas
- Current is charge derivative
- Damped harmonic oscillator equation
- Density from mass and volume
- Electrical conductance is inverse resistance
- Harmonic oscillator is a second order derivative equation
- Heat capacity ratio
- Impedance is resistance and reactance
- Impulse is integral of force over time
- Intensity of sound wave is rate of energy transfer over area
- Linear coefficient of thermal expansion
- Lorentz factor
- Mass flow rate
- Mass fraction of mixture component
- Mechanical energy is kinetic and potential energy
- Momentum is mass times speed
- Net force is sum of individual forces
- Number density is number of objects per unit volume
- Period from angular frequency
- Power is energy derivative
- Quality factor is ratio of energies
- Radiant exitance is radiant flux emitted per unit area
- Relative refractive index is ratio of wave speeds
- Rotational inertia is mass times squared radius
- Sound level in decibels
- Speed is distance derivative
- Temporal frequency from period
- Temporal frequency is number of events per unit time
- Thermal de Broglie wavelength
- Thermal resistance to conduction
- Thermodynamic compressibility
- Volumetric coefficient of thermal expansion
- Wave equation in one dimension
- Conditions
- Physical symbols
- Astronomy (Symbols)
- Basic (Symbols)
any_quantitytimeperiodmassmolar_massworkenergy_densityspectral_energy_densityenergyspecific_energypowerradius_of_curvaturedensitylinear_densityintensitywhole_numberpositive_numbernonnegative_numbernumber_densityparticle_countangleprobabilityfractional_changeexponential_decay_constantcharacteristic_lengthmolar_volume
- Chemistry (Symbols)
- Classical mechanics (Symbols)
forcetensionspeedaccelerationpositioneuclidean_distancedistancedistance_to_origindistance_to_axislengthradiusdiametersemimajor_axissemiminor_axisthicknessareaarc_lengthangular_speedangular_frequencyangular_accelerationangular_distanceangular_wavenumberwavelengthdamping_ratiovolumeimpulsephase_speedgroup_speedpressuretemporal_frequencysound_intensity_levelrotational_inertiaquality_factormomentummechanical_energykinetic_energypotential_energymass_flow_ratestiffnesscomplianceyoung_modulusphase_shiftphasefriction_coefficientheighttorquetorsion_stiffnessbulk_moduluspoisson_ratioengineering_normal_straindeformationstrainstressmach_numberdiffusion_coefficientdynamic_viscositydiffusion_fluxdegrees_of_freedomangular_momentumlatitudelongitudesector_speedkepler_constantsurface_tension
- Electrodynamics (Symbols)
admittanceelectrical_conductancesusceptanceelectrical_impedanceelectromotive_forcemagnetic_fluxabsolute_permittivityrelative_permittivityabsolute_permeabilityrelative_permeabilitycapacitancechargevoltagecurrentelectrical_resistanceelectric_dipole_momentelectric_field_strengthsurface_charge_densityelectric_fluxmagnetic_flux_densityelectric_potentialpower_factorelectrical_resistivityinductanceelectric_time_constantelectrical_reactancecurrent_densityemissivitymagnetic_momentelectric_displacementattenuation_coefficientmagnetic_field_strengthelectrical_conductivity
- Optics (Symbols)
- Quantum Mechanics (Symbols)
- Relativistic mechanics (Symbols)
- Thermodynamics (Symbols)
temperatureadiabatic_indexheat_capacitymolar_heat_capacitythermal_expansion_coefficientthermodynamic_compressibilitythermal_resistancethermal_conductivitythermal_insulancecompressibility_factorpartition_functionboltzmann_factorentropychemical_potentialgibbs_energyenthalpyhelmholtz_free_energyinternal_energythermal_wavelengthheatthermal_efficiencystatistical_weightrelative_humiditymean_free_pathsutherland_constantprandtl_numbergrashof_numberkinematic_viscositythermal_diffusivityattractive_forces_parameterexcluded_volume_parameter
- Physical constants
standard_conditions_temperaturestandard_laboratory_temperatureelectron_rest_massbohr_radiushydrogen_ionization_energysolar_massearth_massboltzmann_constantmolar_gas_constantspeed_of_lightvacuum_permittivityvacuum_permeabilityelementary_chargehbarplanckavogadro_constantacceleration_due_to_gravitystefan_boltzmann_constantrichardson_constantrydberg_frequencywien_displacement_constantgravitational_constanthubble_constantzero_point_luminositysun_luminosityfaraday_constant