Advanced Placement Physics C Table of Information

ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS m p 1.67 ´ 1027 kg Proton mass, = e 1.60 ´ 1019 C Electron charge magnitude, = Neutron mass, = mn 1.67 ´ 1027 kg Electron mass, = me 9.11 ´ 1031 kg Avogadro's number, = N0 6.02 ´ 1023 mol 1 R  8.31 JI (mol.K) Universal gas constant, Boltzmann's constant, = kB 1.38 ´ 10 23 eV 1.60 ´ 1019 J 1 electron volt, 1= Speed of light, = c 3.00 ´ 108 mI s Universal gravitational = G 6.67 ´ 1011 N m2 constant, Acceleration due to gravity g  9.8 m s2 at Earth's surface, I JI K h= 6.63 ´ 10 Planck's constant, hc =´ 1.99 10 34 25 = e0 8.85 ´ 10 Vacuum permittivity, Vacuum permeability, Magnetic constant, k ¢= UNIT SYMBOLS Factor PREFIXES Symbol Prefix K mole, hertz, newton, pascal, joule, mol Hz N Pa J giga G 106 mega M cosq 1 103 kilo k tanq 0 10 2 centi C 10 3 milli m 10 6 micro m 10 9 nano n pico p 164 | Appendix V.1 J m =´ 1.24 10 eV.nm . C2 N m2 2 2 . NI m2 = 1.0 ´ 105 Pa m0 I  4p = 1 ´ 107 (T m)I A watt, coulomb, volt, ohm, henry, farad, tesla, degree Celsius, electron volt, w C V W H F T °C eV VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES  q 30 0 37 45 53 60 90 3I 5 4I 5 1I 2 sinq 2 2 3 2 0 1 10 9 10 12 . 3 m= 4p ´ 107 (T.m)I A 0 1 atm = 1.0 ´ 105 1 atmosphere pressure, J.s = 4.14 ´ 1015 eV s I .   N.m IC 12 k 1I  4pe= 9.0 ´ 109 Coulomb's law constant, = 0 m kg s A I 1u = 1.66 ´ 1027 kg = 931 MeV c2 1 unified atomic mass unit, meter, kilogram, second, ampere, kelvin,  .  I kg2 3 2 r; 3 3 r; 4I 5 3I 4 r; 2 2 r; 3I 5 1I 2 0 1 4I 3 3 ✓ ¥ r; The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges would drift. III. The electric potential is zero at an infinite distance from an isolated point charge. IV. All batteries and meters are ideal unless otherwise stated. V. Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated. AP Physics C: Mechanics Course and Exam Description ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS  Ãx Ãx 0  a x t 1 2 at 2 x x x0  Ãx 0 t  Ãx2 Ãx02  2ax  x  x0   a F   J Fnet F å  m m dp dt F dt ò Dp p  mv IF-f I £ m 1~FN I D E W  K  1 2 mà 2 P dE dt òF dr P F v DUg  mg Dh a c à  w2 r r  I åt  I Us  r dm ò xcm   T å mr 2p  w 2 å mi xi å mi Ts  2 p Tp  2p à  rw L = r ´ p = Iw K  1 2 k  Dx  2  x xmax cos(wt  f t net I 2 a = acceleration E= energy F= force f = frequency h = height I = rotational inertia J = impulse K= kinetic energy k = spring constant £ = length L = angular momentum m= mass P= power p = momentum r = radius or distance T= period t = time U= potential energy v = 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 = phase angle Fs  k D x 2 t= r ´ F  a ELECTRICITY AND MAGNETISM 1 2 Iw 2 IF-G I  1 f F m k f g Gm1m2 UG   r2 Gm1m2 r  w w0  at q q0  w0t  1 2 at 2 A= area B= magnetic field 1 q1q2 4pe0 r 2 FE  E  FE q òE dA  C= capacitance d = distance E= electric field e = emf F= force I = current J = current density L = inductance  = length n = number of loops of wire per unit length N= number of charge carriers per unit volume P= power Q= charge q = point charge R= resistance r = radius or distance t = time U= potential or stored energy V = electric potential v = velocity or speed r = resistivity Q e0 dV dx Ex   ò DV   E dr q 1 4pe0 V  å rii i 1 q1q2 4pe0 r  U qV E Q C DV  ke0 A d C  å Ci Cp  F = flux k = dielectric constant i 1 1 å Cs i Ci FM = qv ´ B ò -. 0 B d £  m0 I dQ I  dt 1  UC  QDV 2 re R A 1 C  DV  2 2 m0 I d £´ r 4p r 2 dB  = F ò I d£ ´ B E  rJ Bs  m0 nI I  Nevd A FB  I  DV R Rs  å Ri 1  Rp i 1 åR i i ò B .dA - . e  0ò E d £   e  L UL  d FB dt dI dt 1 2 LI 2 P  I DV -2- AP Physics C: Mechanics Course and Exam Description Appendix V.1 | 165 ADVANCED PLACEMENT PHYSICS C EQUATIONS CALCULUS GEOMETRY AND TRIGONOMETRY Rectangle A =area C =circumference V =volume S = surface area b =base h =height  = length w =width r =radius s = arc length q = angle A  bh Triangle A 1 bh 2 Circle A  pr2 C  2p r s  rq Rectangular Solid Cylinder V  pr2 q 2 166 a b | Appendix V.1 dx  1 n 1 x , n ¹ -1 n 1 1 ax e a ln x  a 1 ò cos  ax dx  a sin  ax ò sin  ax dx  a 2  b2  c2 tan q  ax dx Right Triangle b c d  sin  ax   a cos  ax dx ò x  a S  4p r 2 cos q  d  ln ax  1 dx x òe 4 V  pr3 3 a c d ax  e   aeax dx n = ò x dx Sphere sin q  d n  x   nxn 1 dx d  cos  ax   a sin  ax dx V  f wh  S 2p r  2p r df d f du  dx du dx 1  cos  ax a VECTOR PRODUCTS ~a ~ b A•B  AB cos q A´B = AB sin q AP Physics C: Mechanics Course and Exam Description