ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS Proton mass, m p 1.67 10 27 kg Neutron mass, mn 1.67 10 27 kg Electron mass, me 9.11 10 31 kg 6.02 10 23 mol 1 Avogadro’s number, N 0 R Universal gas constant, 8.31 J (mol <K) 1.60 10 19 C 1 electron volt, 1 eV 1.60 10 19 J Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, 3.00 108 m s c 6.67 10 11 N<m 2 G kg 2 9.8 m s2 g 1.38 10 23 J K Boltzmann’s constant, k B 1 unified atomic mass unit, 1u 1.66 10 27 kg 931 MeV c 2 Planck’s constant, h 6.63 10 34 J <s 4.14 10 15 eV <s hc 1.99 10 25 J <m 1.24 103 eV < nm e0 8.85 10 12 C2 N < m 2 Vacuum permittivity, Coulomb’s law constant, k Magnetic constant, k 1 atmosphere pressure, meter, kilogram, second, ampere, kelvin, PREFIXES Factor Prefix Symbol m kg s A K mole, hertz, newton, pascal, joule, 1 4 pe0 m0 Vacuum permeability, UNIT SYMBOLS e Electron charge magnitude, m0 4 p 1 atm mol Hz N Pa J 9.0 109 N< m 2 C2 4 p 10 7 (T <m) A 1 10 7 (T< m) A 1.0 105 N m 2 watt, coulomb, volt, ohm, henry, W C V W H 1.0 105 Pa farad, tesla, degree Celsius, electron volt, F T C eV VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES D q 0 30D 37D 45D 53D 60D 90D 109 giga G sin q 0 12 35 2 2 45 3 2 1 106 mega M cos q 1 3 2 45 2 2 35 12 0 103 kilo k tan q 0 3 3 34 1 43 3 10 2 centi c 10 3 milli m 6 micro m 10 9 nano n 10 12 pico p 10 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. ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS Ãx Ãx 0 a x t x x0 Ãx 0 t Ãx2 a F J p 2 Ãx 0 2 a x x x0 m dp dt Ô F dt m FN Ô F dr W K 1 2 mà 2 dE dt F v DUg ac t a I mg Dh Ã2 r w2r Us rF Çt I x t net I 2 Ô r dm Ç mr à rw L r p 1 2 Iw 2 w0 at q q0 w0 t 1 k Dx 2 2 xmax cos( wt f FE E Ex DV V ε Q e0 dV dx Ô E dr DV Q C k e0 A d Cp Ç Ci 1 Cs ÇC 1 i i E Tp 2p g I I R FG Gm1m2 r2 Gm1m2 r Rs 1 Rp P area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance radius or distance time potential or stored energy electric potential velocity or speed resistivity flux dielectric constant qv B Ô B d dQ dt m k 1 f = = = = = = = V= v = r = F = k = FM i 2p 2p w P Q q R r t U 1 q1q2 4pe0 r C = = = = = = = = = = = = N = q Ç rii i 1 4pe0 qV UC F I J L n UE I A B C d E FE q Ts UG 1 2 at 2 1 q1q2 4pe0 r 2 Ô E dA 2 Iw w acceleration energy force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration phase angle k D x 1 QDV 2 r A rJ T Ç mi xi Ç mi xcm K Dp mv DE P Fnet m ÇF Ff P 1 2 at 2 x a = E= F = f = h = I = J = K = k = = L = m= P = p = r = T = t = U= v = W= x = m = q = t = w = a = f = Fs ELECTRICITY AND MAGNETISM 1 C DV 2 2 dB F m0 I m0 I d r 4p r 2 Ô I d B Bs m0 nI Nevd A FB Ô B dA DV R e Ô E d e L Ç Ri i 1 ÇR i I DV i UL dI dt 1 2 LI 2 d FB dt ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY Rectangle A bh 1 bh 2 Circle A pr2 C 2p r s rq Rectangular Solid V wh Cylinder V pr S 2p r 2p r df dx A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius s = arc length q = angle Triangle A CALCULUS S d ax e dx aeax q 2 @ a cos ax d >cos ax dx @ a sin ax Ôe n dx ax dx dx Ôxa 4 3 pr 3 4p r 2 a 2 b2 1 x d >sin ax dx Ôx r Right Triangle 1 n 1 x , n 1 n 1 1 ax e a ln x a Ô cos ax dx 1 sin ax a Ô sin ax dx 1 cos ax a c2 sin q a c cos q b c tan q nx n 1 d ln ax dx Sphere V d n x dx s 2 d f du du dx a b c q a 90° b VECTOR PRODUCTS A B AB cos q AB AB sin q