Physics - Equations & Formulae

TABLE OF INFORMATION FOR 2002 CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit, 1 u 1 66 10 27 == - . kg 931 MeV/2 c Proton mass, mp= × − 167 10 27 . kg Neutron mass, mn= × − 167 10 27 . kg Electron mass, me= × − 911 10 31 . kg Magnitude of the electron charge, e= × − 160 10 19 . C Avogadro’s number, N0 23 1 6 02 10 = × − . mol Universal gas constant, R ¼ 8 31 . /( ) J mol K Boltzmann’s constant, kB= × − 138 10 23 . J/K Speed of light, c= × 3 00 108 . /m s Planck’s constant, h hc= × = × = × = × −− − ⋅ ⋅ ⋅⋅ 6 63 10 414 10 199 10 124 10 34 15 25 3 .. .. J s eV s J m eV nm Vacuum permittivity, 0 12 2 2 885 10 = × − ⋅ . /C N m Coulomb’s law constant, k= = × ⋅ 1 4 90 10 0 9 2 2 /. /πN m C Vacuum permeability, µ π 0 7 4 10 = × − ⋅ ( )/T m A Magnetic constant, k= Tm A 0µ π /( ) /4 107 = − ⋅ Universal gravitational constant, G = ¼ - 6 67 10 11 3 2 . /m kg s Acceleration due to gravity at the Earth’s surface, g = 9 8 2 . m/s 1 atmosphere pressure, 1 10 10 10 105 2 5 atm N/m Pa = × = × .. 1 electron volt, 1 160 1019 eV J = × − . UNITS Name Symbol meter m kilogram kg second s ampere A kelvin K mole mol hertz Hz newton N pascal Pa joule J watt W coulomb C volt V ohm Ω henry H farad F tesla T degree Celsius oC electronvool eV PREFIXES Factor Prefix Symbol 109 giga G 106 mega M 103 kilo k 10 2 − centi c 10 3 − milli m 10 6 − micro µ 10 9 − nano n 10 12 − pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES θ sin θ cos θ tan θ 0o 0 1 0 30o 1/2 3 2 /3 3 /37o 3/5 4/5 3/4 45o 2 2 /2 2 /1 53o 4/5 3/5 4/3 60o 3 2 /1/2 3 90o 1 0 ∞ The following conventions are used in this examination. I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current). III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. *IV. For mechanics and thermodynamics equations, W represents the work done on a system. *Not on the Table of Information for Physics C, since Thermodynamics is not a Physics C topic. ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002 NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM u u u u um u t q pp 00 0 2 2 0 2 0 2 221 2 21 2 12 2 1212 22 1 at x x t at a x x m F N a r rm t K m U mgh W Fr P Wt P F k U kx T mk T g T f F Gm m r U Gm m r net cs spfric g avg sGG F F a p v J F p F F x F sin q u u q D D D D D D r F v cos cos a = acceleration F = force f = frequency h = height J = impulse K = kinetic energy k = spring constant = length m = mass N = normal force P = power p = momentum r = radius or distance r = position vector T = period t = time U = potential energy u = velocity or speed W = work done on a system x = position m = coefficient of friction q = angle t = torque F q q r q U qV q qr E Vd V qr C QV C A d U QV CV I Qt R A V IR P IV C C C C R R R R F q B F BI B Ir BA t B Eavg i i i avg i i BBcp i i s i i s i p i m m === = = − ==== = = ===== == == == = = − = ∑ ∑∑∑∑• 1 4 1 4 1 412 12 1 1 1 1 2 0 1 2 0 1 2 0 0 2 0 2 p p pu mp f f u ee E FB A ρ θ θ θ sin sin cos avg A = area B = magnetic field C = capacitance d = distance E = electric field e = emf F = force I = current = length P = power Q = charge q = point charge R = resistance r = distance t = time U = potential (stored) energy V = electric potential or potential difference u = velocity or speed r = resistivity fm = magnetic flux ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS p p gh F Vg A A p gy T Q mL Q mc T p FA pV nRT K k T RT M k T W pV Q nc T U Q W U nc T e W Q e T T T buoy avg B rms B V H c H C H 0 1 1 2 2 2 0 12 323 3 r r u u r ru m const. D D DD D DD D a u A = area c = specific heat or molar specific heat e = efficiency F = force h = depth Kavg = average molecular kinetic energy L = heat of transformation = length M= molecular mass m= mass of sample n = number of moles p = pressure Q= heat transferred to a system T = temperature U= internal energy V = volume u = velocity or speed urms = root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion µ = mass of molecule r = density u uq q qq l l f n c n n c nn si s f M hi h si s f R d m xm m L d l 1 1 2 2 21 00 0 1 1 1 2 sin sin sinsind = separation f = frequency or focal length h = height L = distance M= magnification m= an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q = angle ATOMIC AND NUCLEAR PHYSICS E hf pc K hf hp E mc = = = − = = max ( ) f lD D 2 E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function GEOMETRY AND TRIGONOMETRY Rectangle Triangle Circle Parallelepiped Cylinder Sphere Right Triangle A bh A bh A r C r V wh V r S r r V r S r a b c acbcab ======= + ==+ = === 12 22 2 434 22 2 3 2 2 2 2 pp pp p p p qqqsin cos tan A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius c a b 90 q ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 MECHANICS ELECTRICITY AND MAGNETISM u u u u umu u w u ww w w a q q w a 00 0 0 0 00 0 12 2 1212 12 2 2 2 2 2 2 2 2 2 2 at x x t at a x x m ddt dt m F N W d K m P dW dt PU mgh a r r I I rdm mr m m r I K I tt t k U net g c net cm sfric F F a F p J F p p vF r F r r L r p F x D D r F v t t t a w s sp kx T f T mk T g Gm m r U Gm m r GG 122 1 22 21 2 21 2 p wpp F ra = acceleration F = force f = frequency h = height I = rotational inertia J = impulse K = kinetic energy k = spring constant = length L = angular momentum m = mass N = normal force P = power p = momentum r = radius or distance r = position vector T = period t = time U = potential energy u = velocity or speed W = work done on a system x = position m = coefficient of friction q = angle t = torque w = angular speed a = angular acceleration F q q r qd Q E dV dr V qr U qV q qr C QV C A d C C C C I dQ dt U QV CV R A V IR R R R R P IVqd I I d B nId ddt L dI i i i E i i Mp i i s i i cs i p i s m m == = = − == = ==== == = ==== == ×= = × == = − = − •• • ∑ ∑∑∑∑1 4 1 4 1 4 1 1 12 12 1 10 1 2 0 0 0 1 2 0 2 0 0 2 pp p kr m m f f ee E F E A F v B BF B B A ø ø dt U LI L = 12 2 A = area B = magnetic field C = capacitance d = distance E = electric field e = emf F = force I = current L = inductance = length n = number of loops of wire per unit length P = power Q = charge q = point charge R = resistance r = distance t = time U = potential or stored energy V = electric potential u = velocity or speed r = resistivity fm = magnetic flux k = dielectric constant ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 GEOMETRY AND TRIGONOMETRY Rectangle Triangle Circle Parallelepiped Cylinder Sphere Right Triangle A bh A bh A r C r V wh V r S r r V r S r a b c acbcab ======= + ==+ = === 12 22 2 43 4 22 2 3 2 2 2 2 pp pp p p p sin cos tan qqq A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius c a b 90 q CALCULUS df dx df du du dx d dxx nx d dxe e d dx x x d dx x x d dx x x x dx n x n e dx e dx x x x dx x x dx x n n x x n n x x - + 1 1n 1n 1 1 1 1 1 sin cos cos sin , cos sin sin cos