General Physics Equation Summary Sheet SI UNITS KINEMATICS Length Mass Time Electric current Temperature Luminous intensity Δx ∆x v= ∆t ∆v a= ∆t No Acceleration Δx = vt m kg s A K Cd DERIVED UNITS m3 N J W Pa C F Volume Force Energy/Work Power Pressure Charge Resistance Capacitance MECHANICS Displacement Velocity Acceleration Uniform Acceleration Δx = vavgt Δx = vit + ½at2 Fg = G vf2 = vi2 + 2aΔx vf = vi + at MOMENTUM AND COLLISIONS p = mv FΔt = Δp momentum Impulse-Momentum Theorem Elastic Collisions Perfectly Inelastic Collisions pi = p f KEi = KEf pi = p f KEi > KEf Linear Angular Relation Δx ∆x v= ∆t ∆v a= ∆t Δθ ∆θ ω= ∆t ∆ω α= ∆t Δx = r Δθ v = rω a = r No Acceleration Uniform Acceleration linear angular linear angular Δx = vt Δθ = ωt ChemistryPrep.com N ∙ m2 kg 2 Gravitational Constant W = mg Weight Ffmax = μs FN Static Friction Ff = μk FN Kinetic Friction Δx = vavgt Δx = vit + ½at2 vf2 = vi2 + 2aΔx vf = vi + at W = (Fcosθ)d E = KE + U KEi + Ui = KEf + Uf KE = ½mv2 Work Mechanical Energy Conservation of Mechanical Energy Kinetic Energy (Translational) Ugravitational = mgy Uelastic = ½kx2 WNC = ΔE Wnet = ΔKE F = -kx W P= = Fv ∆t Gravitational Potential Energy Elastic Potential Energy Work of Nonconservative Forces Work-Energy Theorem Hooke’s Law (Spring Force) Power UNIFORM CIRCULAR MOTION v2 ac = r mv 2 F = ma c = r ROTATIONAL KINEMATICS Acceleration Gravity WORK AND ENERGY 1012 109 106 103 10-2 10-3 10-6 10-9 10-12 10-15 10-18 Displacement Velocity m1 m2 r2 G = 6.67 × 10−11 METRIC PREFIXES Terra Giga Mega kilo centi milli icro nano pico femto atto Newton’s Laws of Motion If F = 0, then v = constant F = ma F1→2 = -F2→1 1st Law 2nd Law 3rd Law Δθ = ωavgt Δθ = ωit + ½t2 ωf2 = ωi2 + 2Δθ ωf = ωi + t Centripetal Acceleration Centripetal Force ROTATIONAL DYNAMICS = F⊥ r = (Fsinθ) r I = ∑mr2 xCG = ∑ mi xi ∑ mi ∑F = 0 ∑τ = 0 Torque Moment of Inertia Center of Gravity Conditions for Equilibrium Angular Linear Δθ ω α I τ τ = I α KErot = ½I2 W = τ(Δθ) L = I d v a m F F = ma KE = ½mv2 W = Fd p = mv 1 ELASTICITY OF SOLIDS F ∆L =Y A L0 F ∆x =S A h ∆P = −B ∆V V Stretching/Compression Shear Deformation S. G. = Volume Deformation P = fluid g h GASES F P= A p1V1 = p2V2 V1 V2 = T1 T2 V1 V2 = n1 n2 p1 V1 p2 V2 = T1 T2 Pressure Boyle’s Law Charles’ Law Avogadro’s Principle Combined Gas Law pV = nRT ptotal = pA + pB + pC + … pA = χA ptotal FLUIDS m ρ= V Perfect Gas Law Dalton’s Law of Partial Pressures SIMPLE HARMONIC MOTION Density ρ P = P0 + fluid g h FB = Wfluid displaced FB=(fluid)(Vsubmerged)(g) ρobject % submerged = × 100 ρfluid F1 F2 = A1 A 2 A1d1 = A2d2 F = Av A1v1 = A2v2 P1 + ½v12 + gy1 = P2 + ½v22 + gy2 q C= ∆T C Cs = m C Cm = n δU ∆U CV = ( ) = δT V ∆T δH ∆H CP = ( ) = δT P ∆T U = q + w x = Acos(ωt) Displacement v = -Aωsin(ωt) vmax = Aω a = -Aω2cos(ωt) amax = Aω2 1 f= T 2π ω = 2πf = T Velocity k ω=√ 𝑚 Frequency Factor for Springs g L x = Acos(ωt + ϕ) Frequency Factor for Pendulums ϕ = phase shift H = U + pV y(x,t) = Acos(ωt ± kx) ω = 2f 2π k= 1st Law Acceleration Frequency / Period Frequency Factor ω=√ Standing Waves f = v 2L n 4L n = n n = Wave Speed n = 1,2,3. .. n = 1,3,5. .. T v=√ μ ChemistryPrep.com String fixed at both ends Pipe open at both ends String fixed at one end Pipe open at one end Wave Velocity on a String Specific Gravity ρ𝐻2𝑂 Hydrostatic Pressure (Gauge Pressure) Absolute Pressure Buoyancy Force Pascal’s Principle (Hydraulic Jack) Hydraulic Jack Flow Rate Continuity Equation Bernoulli’s Equation THERMODYNAMICS Heat Capacity Specific Heat Capacity Molar Heat Capacity Constant Volume Heat Capacity Constant Pressure Heat Capacity Change in Internal Energy q = ∫ CV dT Constant V w = ∫ −pext dV Universal q = ∫ CP dT Constant P w = −p∆V Constant pext q = −w Constant T w = −nRTln H = qp CP – CV = nR Laws of Thermodynamics nd 2 Law Vf Vi Reversible, Isothermal Enthalpy Enthalpy Change at Constant p For a Perfect Gas Energy can’t be created or destroyed. For a spontaneous process, ΔSuniverse > 0. rd 3 Law A perfectly ordered crystal at 0K has zero entropy. qrev Entropy Change ∆S = T Vf pi Entropy Change during ∆S = nRln = nRln Expansion/Compression Vi pf Tf Entropy Change during heating ∆S = nC ln Ti 2 SOUND v = f Y v=√ ρ P v=√ ρ v = 331m/s√ T 273K P P = A 4πr 2 I β = 10log 𝐼0 I= W 𝑚2 v ± 𝑣0 𝑓0 = 𝑓𝑠 v ∓ 𝑣𝑠 DC CIRCUITS Speed of Sound Speed of Sound in a Metal Rod q C= ∆v Speed of Sound in a Gas Q(t) = Q max (1 − e−τ ) Temperature Dependence on the Speed of Sound Capacitance Capacitor Charging t t V(t) = ε (1 − e−τ ) Intensity of Sound Intensity Level I(t) = ε −t e τ 𝑅 Capacitor Discharging 𝐼0 = 10−12 Doppler Effect ELECTRIC FIELDS AND FORCES e = 1.602×10-19C 𝑞1 𝑞2 F = |𝑘 2 | 𝑟 F = qE 𝑞 E = |𝑘 2 | 𝑟 Q 𝐸 = EAcosθ = ϵo q V=k r U = qV ΔV = -Ed W = qΔV W = -qΔV t Q(t) = Q max e−τ t V(t) = ε e−τ Fundamental charge Coulomb’s Law Force due to an Electric Field Electric Field due to a Point Charge Gauss’s Law (Electric Flux) Potential due to a Point Charge Potential Energy of a Point Charge Relationship between ΔV and E Work done against an electric field Work done by an electric field I(t) = ε −t e τ 𝑅 C = ε0 A d A C = (ε0 ) d 1 1 Ustored = C∆V 2 = Q∆V 2 2 1 1 1 = + +. .. Ceq C1 C2 Ceq = C1 + C2 +. .. ∆q I= ∆t ΔV = IR L R=ρ A = 0(1 + ΔT) R = R0(1 + ΔT) P = ∆VI = I 2 R = ChemistryPrep.com Parallel Plate Capacitor ∆V 2 R Potential Energy Stored by a Capacitor Capacitors in Series Capacitors in Parallel Current Ohm’s Law Resistance of a Wire Temperature Dependence of the Resistivity and Resistance Power Dissipated by a Resistor R eq = R + R 2 +. .. 1 1 1 = + +. .. R eq R R 2 Current entering a junction = Current exiting a junction Resistors in Series Resistors in Parallel The potential difference around any closed loop sums to zero. Kirchoff’s Loop Rule Kirchoff’s Junction Rule 3 MAGNETIC FIELDS AND FORCES F = qvBsinθ Magnetic Force on a Charged Particle in Motion Magnetic Force on a Current-carrying Wire F = BI sinθ INDUCED VOLTAGES AND INDUCTANCE B = B⊥A = BAcosθ ∆B ε = −N ∆t ΔV = B v⊥ ε = NBAω sinωt ∆B21 ∆I ε1 = −N1 = −M ∆t ∆t Magnetic Flux Faraday’s Law (Induce Emf) Motional Emf Generator Emf Mutual Inductance ∆B12 ∆I = −M ∆t ∆t ∆B ∆I ε = −N = −L ∆t ∆t ε2 = −N2 τ = BIANsinθ B= Torque on a CurrentCarrying Loop Magnetic Field Due to a Current Carrying Wire μ0 I 2πr μ0 I B=N 2R B= Magnetic Field at the Center of a Circular Current-Carrying Loop μ0 NI = μ0 nI L ∆B ∆B =N ∆I I ΔV1I1 = ΔV2I2 ∆𝑉1 𝑁1 𝐼2 = = ∆𝑉2 𝑁2 𝐼1 ∆I ε = −L ∆t L=N I(t) = AC Potential Rms Potential Rms Current Power Dissipated in a Resistor Ohm’s Law Capacitive Reactance ΔVC,rms = Irms XC XC = 2πfL Inductive Reactance ΔVL,rms = Irms XL + (XL − XC ΔVmax = Imax Z ΔVrms = Irms Z 1 f0 = 2π√LC ChemistryPrep.com Emf in an RL Circuit τ= PEL = ½ LI2 AC (ALTERNATING CURRENT) CIRCUITS Z= t ε (1 − e−τ ) R Transformers L R Current in an RL Circuit Potential Energy Stored in an Inductor Magnetic Field Inside an Ideal Solenoid ΔV = ΔVmax sinωt ∆Vmax ∆Vrms = √2 ∆𝐼𝑚𝑎𝑥 ∆I𝑟𝑚𝑠 = √2 P = Irms2 R ΔVmax = Imax R ΔVrms = Irms R 1 1 XC = = 2πfC ωC √R2 Self-Inductance )2 Impedance of RLC Circuits Resonance Frequency in LC Circuits c= 1 ELECTROMAGNETIC RADIATION √ε0 μ0 = 3.0 × 108 m c n= v λf = v Ephoton = hf 1 uE = ε0 E 2 2 1 2 uB = B 2μ0 P I= A u fO = fS (1 ± ) c 1 I = I0 2 I = I0 cos 2 θ Speed of Light in a Vacuum /s Index of Refraction Wavelength/Frequency of Light Energy of a Photon Energy density of the Electric Field Energy density of the Magnetic Field Intensity of Light Doppler Effect Unpolarized light transmitted through a polarizing filter Polarized light transmitted through a polarizing filter 4 REFLECTION AND REFRACTION θincidence = θreflection n1 sinθ1 = n2 sinθ2 c n= v 𝑛2 sinθ𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = 𝑛1 𝑛2 d′ = 𝑑 𝑛1 Law of Reflection Snell’s Law of Refraction Index of Refraction Critical Angle for Total Internal Reflection Apparent depth MIRRORS AND LENSES f=½R 1 1 1 + = 𝑝 𝑞 𝑓 ℎ𝑖 𝑞 m= =− ℎ𝑜 𝑝 Focal Length Thin Mirror and Lens Equation Magnification 𝐿𝑒𝑛𝑠 𝑃𝑜𝑤𝑒𝑟 = f number = 𝑓 𝐷 1 𝑓𝑚 a sinθdark = m Dark Fringes (Double Slit Interference) Thin Film Interference Destructive Interference (No Phase Shift) Thin Film Interference Destructive Interference (Phase Shift) Bright Fringes (Diffreaction Grating) Dark Fringes (Single Slit Interference) CONSTANTS 2 9.80 m/s F number G 6.67×10-11 N∙m2/kg2 Gravitational acceleration near the surface of the Earth Gravitational constant ME RE R ke 0 e 5.98×1024 kg 6.38×106 m 8.314 J/mol∙K 8.99×109 N∙m2/C2 8.85×10-11 C2/N∙m2 1.62×10-31 C Mass of the Earth Radius of the Earth Universal gas constant Coulomb constant Permitivity of Free Space Fundamental charge me mp 9.11×10-31 kg 1.67×10-27 kg 0 c 4×10-7 T∙m/A 3.00×108 m/s Mass of an electron Mass of a proton Permeability of Free Space Speed of Light (vacuum) f q virtual Converging Mirror/Lens p>f real p<f virtual real, inverted image virtual, upright image q d sinθbright = m Bright Fringes (Double Slit Interference) g Always q d sinθbright = m L ybright = m d d sinθdark = (m + ½) L 1 ybright = (m + ) d 2 1 2t = (m + ) film 2 2t = mfilm Lens Power Diverging Mirror/Lens p WAVE OPTICS upright m inverted m |𝑚| < 1 reduced image |𝑚| > 1 enlarged image Combinations of Lenses m = (m1)(m2) 1 1 1 = + 𝑓𝑛𝑒𝑡 𝑓1 𝑓2 1 1 1 𝑑 = + + 𝑓𝑛𝑒𝑡 𝑓1 𝑓2 𝑓1 𝑓2 magnification Two lenses in direct contact Two lenses not in direct contact Optical Instruments M1 = − 𝑚𝑒 = m= ≈ 𝐿 𝑝1 𝑓𝑜 25𝑐𝑚 𝑓𝑒 θ 𝑓𝑜 = θo 𝑓𝑒 θ𝑚𝑖𝑛 ≈ θ𝑚𝑖𝑛 𝑞1 𝑎 1.22 ≈ 𝐷 ChemistryPrep.com Lateral magnification of objective Angular magnification of eyepiece Angular magnification of a telescope Telescope Resolution (Single Slit) Telescope Resolution (circular aperture ) 5