PHYSICAL CONSTANTS There are a number of physical constants that are used in equations to solve problems in physics. Errors may occur because the dimensionality and/or units of the physical constant are not known. The table below presents some physical constants with their typical symbol, dimension, nominal value and unit of measure in the MKS system. PHYSICAL CONSTANT SYMBOL DIMENSION MKS VALUE UNIT _________________ ______ _________ _________ ____ 3 3 air density, normal rho M/L 1.293 Kg/m conditions air molecule, mass m M 4.81E-26 Kg a air molecule, w M 0.028952 Kg/mole kilogram molecular weight 2 2 atmospheric pressure A M/LT 1.01325 newton/m Avogadro's number N none 6.023E+23 molecules in molecules in a mole a mole 2 2 o Boltzmann's constant k ML /T K 1.380E-23 joule/ K 2 2 electron volt e ML /T 1.60210E-10 joule 3 2 2 2 2 electrostatic constant k ML /T Q 8.987E+9 nt m/coulomb reciprocal permittivity m/farad elementary charge e Q 1.6021892E-19 coulomb electron mass m M 9.1066E-31 Kg e faraday f L/T 9.648456E+4 coulomb/mole 2 2 o gas constant of a mole R ML /T K 8.3144 joule/ K PHYSICAL CONSTANT SYMBOL DIMENSION MKS VALUE UNITL _________________ ______ _________ _________ ____ 2 2 gravity (earth) g L/T 9.80665 m/sec hydrogen atom mass m M 1.6734E-27 Kg h hydrogen atom w M 1.0079E-3 Kg/mole kilogram atomic weight 2 2 impedance of free space Z ML /TQ 120Pi ohm 0 mechanical equivalent J none 4186.05 joule/ of heat Kg calorie 2 2 3 permittivity (vacuum) epsi T Q /ML 8.854E-12 farad/meter 0 2 permeability (vacuum) mu ML/Q 4Pi E-7 henry/meter 0 Pi, ratio of circumference Pi none 3.14159265 radians to diameter 2 Planck's constant h ML /T 6.624E-34 joule second speed of light (vacuum) c L/T 2.99792458E+8 meter/second speed of sound (air) s L/T 331.45 meter/second 2 2 2 2 universal gravitational G L /MT 6.6720E-12 nt m /Kg constant Note: some constants are related to combinations of other constants : electrostatic constant = 1/ 4Pi permittivity (vacuum) speed of light = 1/ sqrt( permittivity x permeability ) impedance of free space Z = sqrt( permeability / permittivity ) 0 SOME EQUATIONS OF PHYSICS F = m a force equals mass times acceleration, Newton's second law of motion 2 F = m v /r force equals mass times velocity squared over radius, centripetal force of a mass traveling in a circle 2 F = G m m /s gravitational force between mass and mass at distance s 1 2 1 2 with universal gravitational constant G 2 g = G m /r acceleration due to gravity on earth earth earth 2 F = k Q Q /s electrical force between charge and charge at distance s 1 2 1 2 with electrostatic constant k . If there is a dielectric then multiply by the non dimensional dielectric constant. F = 1/2Pi mu I I /s 1 2 electrical force between two parallel wires carrying currents I and I with a spacing s with permeability 1 2 mu. This is the force for one meter of wire length. 2 F = B H s electrical force in a magnetic field equals the magnetic flux times the magnetic intensity applied to an area 2 F = E D s electrical force in an electric field equals the electric field intensity times the electric displacement applied to an area s = v t distance equals velocity times time (linear) v = a t velocity equals acceleration times time (linear) 2 s = s + v t + 1/2 a t 0 0 linear distance equals initial distance plus initial velocity times time plus one half acceleration times time squared 2 v = sqrt( v + 2as) f 0 the final velocity equals the square root of the initial velocity squared plus two times the acceleration times the distance traveled v = sqrt( s g ) the critical velocity for any object to orbit at a c distance s from the source of gravitational field g theta = omega t angle equals angular velocity times time (rotational) omega = alpha t angular velocity equals angular acceleration times time (rotational) 2 theta = theta + omega t + 1/2 alpha t 0 0 angular rotation equals initial angle plus initial angular velocity times time plus one half angular acceleration times time squared 2 w = sqrt(w + 2 alpha O-) f 0 the final angular velocity equals the square root of the initial angular velocity squared time twice the angular acceleration times the angle traveled E = I R voltage equals current through a resistor times the resistance I = C (E - E )/(t - t ) 2 1 2 1 the current through a capacitor equals the capacitance times the change in voltage over the change in time E = L (I - I )/(t - t ) 2 1 2 1 the voltage across an inductor equals the inductance times the change in current over the change in time C = epsi A/s the capacitance in farad of a parallel plate capacitor equals the permittivity times the area divided by the spacing. L = n mu r (ln 8r/d - 7/4) the inductance in henry of n turns of wire with diameter d closely wrapped in a coil of radius r with permeability mu is approximately given by this equation. H = 1/2 I / r the magnetic intensity at the center of a current loop equals 1/2 the current divided by the radius of the loop B = mu H the magnetic flux equals the permeability times the magnetic intensity D = epsi E the electric displacement equals the permittivity times the electric field intensity P = E I power equals an electrical potential causing a current P = F s power equals a force applied over a distance 2 E = m c energy from converting a mass to energy ( c = speed of light) 2 E = 1/2 m v kinetic energy of a mass traveling at a velocity E = m g s potential energy of a mass in a gravitational field at a height s E = 1/2 B H V energy of a magnetic field in the volume V with magnetic flux B and magnetic intensity H. This is usually an integral of an incremental volume times B times H in the incremental volume. E = 1/2 D E V energy of an electric field in the volume V with electric displacement D and electric field intensity E. This is usually an integral of an incremental volume times D times E in the incremental volume. 2 E = 1/2 C V energy stored in a capacitor with capacitance C having a voltage V 2 E = 1/2 L I energy stored in an inductor with inductance L having a current I T = F s torque equals the force applied at radius s T = I alpha torque equals the rotational inertia times the angular acceleration 2 E = P V = R T = N k T = 1/3 N m v ideal gas law rms These relations are for one mole (kilogram molecule) of an ideal gas at an absolute pressure P, volume V, gas constant R, Avogadro's number N, Boltzmann's constant k, temperature T in degrees kelvin, gas molecule mass m, root mean square speed of the molecules v in meters per second. Each section of the equation rms represents energy in joule. 2 2 P + 1/2 rho v + rho g z = P + 1/2 rho v + rho g z 1 1 1 2 2 2 This equation relates pressure P, velocity v and relative height z for a non compressible fluid in a pipe, observed at location 1 and location 2. rho is the density of the fluid and g is the gravitational constant. 2 L = C rho v A / 2 L the lift force equals the dimensionless coefficient of lift times the air density times the velocity squared times the surface area divided by 2. 2 D = C rho v A / 2 D the drag force equals the dimensionless coefficient of drag times the air density times the velocity squared times the surface area divided by 2. nu = mu / rho the kinematic viscosity equals the dynamic viscosity over the density in a fluid P = Q (p - p ) 1 2 the power, P, required to drive a volume rate of flow, Q, from pressure p to pressure p . 1 1 o o C = K - 273.16 degrees centigrade equals degrees kelvin minus 273.16 o o F = ( K -273.16) x 9/5 + 32 degrees Fahrenheit as a function of degrees kelvin