Physics Equation Sheet

Pythagorean theorem a2 + b2 = c2; c = √a2 + b2 a and b - non-hypotenuse lengths of a right triangle c - hypotenuse length Kinematic equation 1 1 d = 2 (vi + vf )t Physics Kinematic equation 2 vf = vi + at G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) kB - Boltzmann constant (1.38 x 10-23 J/K) 1 Δx = vi t + 2 at2 a - acceleration Δx - displacement t - time vi - initial velocity Kinematic equation 4 2 f 2 i v = v + 2aΔx pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) k - Coulomb’s constant (8.99 x 109 N · m2/C2) a - acceleration t - time vi - initial velocity vf - final velocity Kinematic equation 3 g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) Δx - displacement t - time vi - initial velocity vf - final velocity a - acceleration Δx - displacement vi - initial velocity vf - final velocity Newton’s 1st law If velocity is constant: → Fnet = 0 ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) Fnet - net force on an object Newton’s 2nd law → → µ0 - the permeability of free space (4π x 10-7 N/A2) Fnet = ma Fnet - net force on an object m - mass a - acceleration Newton’s 3rd law c - speed of light in a vacuum (3 x 108 m/s) → → FAB = - FBA h - Planck’s constant (6.63 × 10-34 m2 · kg / s) F - force that object A exerts on object B and vice versa Center of mass R - the Rydberg constant (1.097 x 107 m-1) xcenter = m1x1 + m2x2 + ... + mkxk m1+ m2+ ... + mk xcenter - x- or y-axis position for the center of mass mn - mass of a smaller object that comprises a larger whole. xn - x- or y-coordinate of a smaller object comprising the larger whole Static friction Fmax = μsN Fmax - maximum static friction force N - normal force ųs - coefficient of static friction Kinetic friction Fkinetic = μkN Fkinetic - kinetic friction force N - normal force ųk - coefficient of kinetic friction Gravitational formula Fgrav = G m1m2 r2 Fgrav - gravitational force G - universal gravitational constant m - mass of first and second objects Centripetal acceleration v2 a= r Physics G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) Centripetal force mv2 Fc = r kB - Boltzmann constant (1.38 x 10-23 J/K) Fspring = -kx τ = F · d · sin(θ) τ - torque F - applied force d - lever arm (distance from fulcrum) θ - angle between applied force and lever arm Work W = | F | · d · cos(θ) ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) µ0 - the permeability of free space (4π x 10-7 N/A2) Fspring - spring deformation force k - spring constant x - deformation distance from equilibrium Torque pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) k - Coulomb’s constant (8.99 x 109 N · m2/C2) Fc - centripetal force m - mass of an object v - velocity r - distance of an object from the center of orbit Hooke’s law g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) a - centripetal acceleration v - velocity r - distance of an object from the center of orbit W - work F - applied force d - displacement over which the force is applied θ - angle between applied force and displacement Power W P = Δt P - power W - work or change in energy Δt - time c - speed of light in a vacuum (3 x 108 m/s) Kinetic energy h - Planck’s constant (6.63 × 10-34 m2 · kg / s) KE - kinetic energy m - mass v - velocity 1 KE = 2 mv2 Potential energy R - the Rydberg constant (1.097 x 107 m-1) PEgrav = mgh PE - potential energy m - mass g - acceleration due to gravity h - height above ground level Elastic potential energy PEelastic 1 = 2 kx2 PE - potential energy k - spring coefficient x - spring deformation from equilibrium Conservation of energy KEinitial + PEinitial = KEfinal+ PEfinal PE - potential energy KE - kinetic energy Work-Energy theorem W = ΔKE = KEfinal - KEinitial W - work KE - Kinetic energy Work (Pressure-Volume curve) W - Work P - pressure ΔV - volume W = PΔV Kinetic energy of a particle Physics KE - kinetic energy m - mass of a particle vrms - root mean square of velocity 1 KE = 2 mv2rms Kinetic energy of a particle G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) KE - kinetic energy kB - Boltzmann constant T - temperature 3 KE = 2 kBT g - acceleration due to gravity (9.8 m/s2) Root mean square of velocity R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) vrms = vrms - root mean square of velocity R - ideal gas constant T - temperature Mm - molar mass 3RT Mm kB - Boltzmann constant (1.38 x 10-23 J/K) pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) Celsius to Fahrenheit o 5 C = (oF - 32) x 9 k - Coulomb’s constant (8.99 x 109 N · m2/C2) ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) o o 9 F = (oC x 5 ) + 32 C - temperature in Celsius F - temperature in Fahrenheit o C - temperature in Celsius F - temperature in Fahrenheit First law of thermodynamics ΔU = Q - W h - Planck’s constant (6.63 × 10-34 m2 · kg / s) R - the Rydberg constant (1.097 x 107 m-1) o Fahrenheit to Celsius µ0 - the permeability of free space (4π x 10-7 N/A2) c - speed of light in a vacuum (3 x 108 m/s) o ΔU - change in internal energy of the system Q - heat entering the system W - work done by the system Thermal expansion #1 ΔL = aLLΔT ΔL - change in length aL - coefficient of thermal expansion L - original length ΔT - change in temperature Thermal expansion #2 ΔV = aVVΔT ΔV - change in volume aV - coefficient of thermal expansion V - original volume ΔT - change in temperature Ideal gas law PV = nRT P - pressure V - volume n - moles of gas R - ideal gas constant T - temperature Density ρ - density m - mass V - volume m ρ= V Specific gravity ρ ρ - density of substance ρwater - density of water specific gravity = ρ water Physics Pressure P - pressure F - force A - area F G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) P= A Hydrostatic pressure g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) Psub - gauge pressure ρ - density of fluid g - acceleration due to gravity h - submerged depth Psub = ρgh Absolute pressure kB - Boltzmann constant (1.38 x 10-23 J/K) pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) Pabs = Patm + ρgh k - Coulomb’s constant (8.99 x 109 N · m2/C2) ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) Part of object submerged ρobject % submerged = ρliquid · 100 µ0 - the permeability of free space (4π x 10-7 N/A2) c - speed of light in a vacuum (3 x 108 m/s) %submerged - how much of an object is submerged ρobject - density of object ρliquid - density of liquid Buoyant Force Fbuoy = ρVg h - Planck’s constant (6.63 × 10-34 m2 · kg / s) R - the Rydberg constant (1.097 x 107 m-1) Pabs - absolute pressure Patm - atmospheric pressure ρ - density of fluid g - acceleration due to gravity h - submerged depth Fbuoy - buoyant force ρ - density of fluid V - volume of fluid displaced g - acceleration due to gravity Pascal’s law F F P = A1 = A2 2 1 P - Pressure F - force A - area Pascal’s law W = F1d1 = F2d2 W - work F - Force d - displacement Poiseuille’s law Q= πr4ΔP 8ηL Q - flow rate r - radius of the vessel ΔP - change in pressure η - viscosity L - length of the vessel Bernoulli’s law 1 P1 + 2 ρv12 + ρgh1 = 1 P2 + ρv22 + ρgh2 2 P - pressure ρ - density of fluid v - velocity of the fluid g - acceleration due to gravity h - height or depth with respect to ground level Continuity equation Physics v1A1 = v2A2 v - velocity A - area of the vessel Pitot tube G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) 1 Pstag - Pstatic = 2 ρv 2 g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) Resistance R=ρ kB - Boltzmann constant (1.38 x 10-23 J/K) ℓ A R - resistance ρ - resistivity ℓ - length of resistor A - area of resistor Conductance pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) A k - Coulomb’s constant (8.99 x 109 N · m2/C2) Pstag - stagnation pressure Pstatic - static pressure ρ - density of fluid v - velocity of the fluid G=σ ℓ G - conductance σ - conductivity (1/ρ) ℓ - length of conductor A - area of conductor Coulomb’s law ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) µ0 - the permeability of free space (4π x 10-7 N/A2) kq1q2 r2 F= Electric field c - speed of light in a vacuum (3 x 108 m/s) h - Planck’s constant (6.63 × 10-34 m2 · kg / s) F - electrostatic force k - Coulomb’s constant q - charge of a particle r - distance between charges kQ F E = q = r2 R - the Rydberg constant (1.097 x 107 m-1) E - electric field strength F - electrostatic force Q and q - magnitude of charge k - Coulomb’s constant r - distance from the source charge Electric potential energy U= kQq r U - electric potential energy k - Coulomb’s constant Q and q - magnitude of charges r - distance between charges Electric potential (Voltage) U kQ V=q = r V - voltage U - electric potential energy k - Coulomb’s constant Q or q - magnitude of charge r - distance from electric field source Ohm’s law V - voltage I - current R - resistance V = IR Power V2 P = IV = I 2R = R Physics G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) P - power V - voltage I - current R - resistance Current in series Itotal = I1 = I2 = ... = In Itotal - total current In - current through individual parts of the series circuit Voltage in series g - acceleration due to gravity (9.8 m/s2) Vsource = V1 + V2 + ... + Vn R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) kB - Boltzmann constant (1.38 x 10-23 J/K) Resistance in series Rtotal = R1 + R2 + ... + Rn Itotal = I1 + I2 + ... + In Itotal - total current through a circuit with parallel branches In - current through individual branches of the parallel circuit Voltage in parallel ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) µ0 - the permeability of free space (4π x 10-7 N/A2) Rtotal - total resistance for a given series circuit Rn - resistance of an individual component of the series circuit Current in parallel pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) k - Coulomb’s constant (8.99 x 109 N · m2/C2) Vsource - voltage source Vn - Voltage across individual components of the series circuit Vtotal = V1 = V2 = ... = Vn Vtotal - total circuit voltage Vn - Voltage across individual branches of the parallel circuit Resistance in parallel c - speed of light in a vacuum (3 x 108 m/s) h - Planck’s constant (6.63 × 10-34 m2 · kg / s) R - the Rydberg constant (1.097 x 107 m-1) 1 1 1 1 = R + R + ... + R Rtotal 1 2 n Rtotal - total resistance for a given parallel circuit Rn - resistance of an individual component in a parallel branch Capacitance Q C=V C - capacitance Q - charge stored in capacitor V - voltage across capacitor Capacitance A C = ε0 d C - capacitance ε0 - the permittivity of free space A - cross-sectional area of the plates d - distance between the plates Electric field between capacitor plates V E= d E - electric field between the plates V - voltage across the plates d - distance between the plates Capacitance in series 1 Ctotal 1 1 1 = C + C + ... + C 1 2 n Ctotal - total capacitance of a given series circuit Cn - capacitance of individual components of the series circuit Capacitance in parallel Ctotal = C1 + C2 + ... + Cn Physics G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) Magnetic field around a wire B - magnetic field strength µ0 - the permeability of free space I - current through the wire r - distance from the wire µ0I B = 2πr g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) Magnetic force on a charge FB = qvBsin(θ) kB - Boltzmann constant (1.38 x 10-23 J/K) FB = IℓBsin(θ) ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) FB - magnetic force I - current through the wire ℓ - length of the wire B - external magnetic field strength θ - angle between current and magnetic field vectors Period of a mass on a spring µ0 - the permeability of free space (4π x 10-7 N/A2) T = 2π c - speed of light in a vacuum (3 x 108 m/s) h - Planck’s constant (6.63 × 10-34 m2 · kg / s) FB - magnetic force q - magnitude of charge v - velocity of the charge B - external magnetic field strength θ - angle between velocity and magnetic field vectors Magnetic force on a wire pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) k - Coulomb’s constant (8.99 x 109 N · m2/C2) Ctotal - total capacitance in a given parallel circuit Cn - capacitance of individual component in a parallel branch m k T - period m - mass of object attached to spring k - spring constant Period of a pendulum T = 2π L g R - the Rydberg constant (1.097 x 107 m-1) T - period L - length of the pendulum g - acceleration due to gravity Velocity of a wave v - velocity of the wave λ - wavelength f - frequency v = λf Speed of sound Vsound = B ρ v - speed of sound in a medium B - bulk modulus of medium p - density of medium Decibel level I dB = 10log( I ) 0 dB - decibel level I - intensity of given sound I0 - reference intensity Doppler effect (v +v ) f΄= f0 (vsound + vobserver) sound source f΄- perceived frequency f0 - frequency emitted by the source vsound - speed of sound vobserver - relative velocity of the observer vsource - relative velocity of the source Standing wave for a string or pipe open at both ends Physics λ - wavelength L - length of the pipe or string n - integer of harmonic 2L λ= n Standing wave for a pipe closed at one end G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) λ - wavelength L - length of the pipe nodd - integer of harmonic (odd only) 4L λ= n odd Energy of an electromagnetic wave E - energy of the wave λ - wavelength f - frequency c - speed of light in a vacuum h - Planck’s constant hc E = hf = λ kB - Boltzmann constant (1.38 x 10-23 J/K) pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) k - Coulomb’s constant (8.99 x 109 N · m2/C2) Refractive index n - index of refraction of a medium c - speed of light in a vacuum v - speed of light in the medium c n= v Snell’s law ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) µ0 - the permeability of free space (4π x 10-7 N/A2) n1sin(θ1) = n2sin(θ2) n - index of refraction of each medium θ - angle of incidence and angle of refraction Single-slit diffraction c - speed of light in a vacuum (3 x 108 m/s) h - Planck’s constant (6.63 × 10-34 m2 · kg / s) A - aperture width λ - wavelength m - the order of the minimum θ - angle relative to the original direction of the light Asin(θ) = mλ R - the Rydberg constant (1.097 x 107 m-1) Double-slit diffraction maximum D - distance between apertures n - the order of the maximum λ - wavelength θ - angle relative to the original direction of the light Dsin(θ) = nλ Double-slit diffraction minimum 1 Dsin(θ) = (n + ) λ 2 D - distance between apertures n - the order of the minimum λ - wavelength θ - angle relative to the original direction of the light Thin lens equation 1 = o1 + 1i f f - focal distance o - object distance i - image distance Magnification i m=-o Physics Power of a lens 1 P= f G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) E = mc2 KEmax = Eincident - Ework KE - kinetic energy of ejected electron Eincident - energy of incident photon Ework - energy required to eject an electron Rydberg equation 1 1 1 = R ( 2- 2 ) λ n1 n 2 R - the Rydberg constant n - orbital levels λ - wavelength of photon Alpha decay A A-4 4 ZX → Z - 2 Y + 2 a A - atomic mass Z - atomic number a - alpha particle (helium nucleus) Beta-minus decay µ0 - the permeability of free space (4π x 10-7 N/A2) c - speed of light in a vacuum (3 x 108 m/s) E - binding energy of a nucleus m - mass defect c - speed of light in a vacuum Photoelectric effect k - Coulomb’s constant (8.99 x 109 N · m2/C2) ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) P - power of a lens f - focal distance Mass-energy equivalence kB - Boltzmann constant (1.38 x 10-23 J/K) pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) o - object distance i - image distance m - magnification A A 0 ZX → Z + 1 Y + 0 β A - atomic mass Z - atomic number β- - electron Beta-plus decay h - Planck’s constant (6.63 × 10-34 m2 · kg / s) R - the Rydberg constant (1.097 x 107 m-1) 0 + A A ZX → Z - 1 Y + 0 β A - atomic mass Z - atomic number β+ - positron Gamma decay A A ZX * → ZX + c A - atomic mass Z - atomic number c - high energy radiation Electron capture A A ZX + e → Z - 1 Y A - atomic mass Z - atomic number Exponential decay n = n0e-λt n - remaining amount n0 - original amount t - time λ - decay constant Half-life t1/2 = Physics G - universal gravitational constant (6.67 x 10-11 N · m2 / kg2) g - acceleration due to gravity (9.8 m/s2) R - ideal gas constant (8.3145 J · mol-1 · K-1) or 0.082 L · atm · K-1 · mol-1) kB - Boltzmann constant (1.38 x 10-23 J/K) pwater - density of water (1 g/cm3 = 1 g/ml = 1000 kg/m3) k - Coulomb’s constant (8.99 x 109 N · m2/C2) ε0 - the permittivity of free space (8.85 x 10-12 C2/N · m2) µ0 - the permeability of free space (4π x 10-7 N/A2) c - speed of light in a vacuum (3 x 108 m/s) h - Planck’s constant (6.63 × 10-34 m2 · kg / s) R - the Rydberg constant (1.097 x 107 m-1) 0.693 λ λ - decay constant t1/2 - half-life