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TABLE OF INFORMATION FOR 2002 CONSTANTS AND CONVERSION FACTORS UNITS PREFIXES = 1.66 10 -27 kg Name Symbol Factor Prefix Symbol 1 unified atomic mass unit, 1u meter m 10 9 giga G = 931 MeV/c 2 kilogram kg 10 6 mega M Proton mass, m p = 1.67 × 10 −27 kg Neutron mass, mn = 1.67 × 10 −27 kg second s 10 3 kilo k Electron mass, me = 9.11 × 10 −31 kg −2 ampere A 10 centi c Magnitude of the electron charge, e = 1.60 × 10 −19 C 10 −3 milli m kelvin K Avogadro’s number, N0 = 6.02 × 10 23 mol −1 mole mol 10 −6 micro µ Universal gas constant, R = 8.31 J / ( mol ¼ K ) hertz Hz 10 −9 nano n Boltzmann’s constant, k B = 1.38 × 10 −23 J / K newton N −12 Speed of light, c = 3.00 × 10 8 m / s 10 pico p Planck’s constant, h = 6.63 × 10 −34 J ⋅ s pascal Pa VALUES OF TRIGONOMETRIC FUNCTIONS = 4.14 × 10 −15 eV ⋅ s FOR COMMON ANGLES joule J hc = 1.99 × 10 −25 J ⋅ m watt W θ sin θ cos θ tan θ = 1.24 × 10 3 eV ⋅ nm coulomb C 0 o 0 1 0 Vacuum permittivity, 0 = 8.85 × 10 −12 C / N⋅m 2 2 volt V 30o 1/2 3 /2 3 /3 Coulomb’s law constant, k = 1 / 4π 0 = 9.0 × 10 N ⋅ m / C 9 2 2 ohm Ω Vacuum permeability, µ 0 = 4π × 10 −7 (T ⋅ m ) / A henry H 37o 3/5 4/5 3/4 Magnetic constant, k = µ 0 / 4π = 10 (T ⋅ m ) / A −7 farad F tesla T 45o 2 /2 2 /2 1 Universal gravitational constant, G = 6.67 10 -11 m 3 / kg ¼ s 2 degree Acceleration due to gravity at the Earth’s surface, g = 9.8 m / s 2 Celsius o C 53o 4/5 3/5 4/3 1 atmosphere pressure, 1 atm = 1.0 × 10 5 N / m 2 electron- volt eV 60o 3 /2 1/2 3 = 1.0 × 10 5 Pa 1 electron volt, 1 eV = 1.60 × 10 −19 J 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 0 + at a = acceleration 1 q1 q 2 A =area F= F = force 4p 0 r2 B =magnetic field 1 2 x = x0 + u0 t + at f = frequency C =capacitance 2 F h = height E= d =distance u 2 = u 0 2 + 2a x - x 0 0 5 J = K = impulse kinetic energy q 1 q1 q 2 E = e emf = electric field k = spring constant UE = qV = F =force 4p r Ê F = Fnet = ma l = length 0 I =current m= mass E avg = − V l =length F fric mN N = normal force d P =power P = power = Q charge ∑r 1 qi u2 p = momentum V= q =point charge ac = 4p r r = radius or distance 0 i i R =resistance t = rF sin q r = position vector Q r =distance C= T = period V t =time p = mv t = time 0A = U potential (stored) energy U= potential energy C= V =electric potential or d J = FDt = Dp u = velocity or speed potential difference 1 1 u = velocity or speed W= work done on a system Uc = QV = CV 2 1 x = position 2 2 r = resistivity K = mu 2 m= fm = magnetic flux 2 coefficient of friction DQ q = angle I avg = Dt DUg = mgh t = torque ρl R= W = F Dr = FDr cos q A V = IR Pavg = W P = IV Dt C p = ∑ Ci P = F v = Fu cos q i 1 1 =∑ Fs = - k x Cs i Ci 1 2 Rs = ∑ Ri Us = kx i 2 1 1 m =∑ Ts = 2 p Rp i Ri k l FB = qu B sin θ Tp = 2 p g FB = BIl sin θ 1 m0 I T = B= f 2p r Gm1m2 FG = - fm = B • A = BA cos θ r2 Dfm UG = - Gm1m2 eavg = − r Dt e = Blu ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS p = p0 + rgh A = area u = fl d = separation Fbuoy = rVg c = specific heat or molar c f = frequency or focal n = A1u1 = A2 u 2 specific heat u length e = efficiency n 1 sin q1 = n 2 sin q 2 h = height 1 p + rgy + ru 2 = const. F = force n2 L = distance 2 h = depth sin q c = M= magnification D l = a l 0 DT Kavg = average molecular n1 m = an integer Q = mL kinetic energy 1 1 1 n = index of refraction + = L = heat of transformation si s0 f R = radius of curvature Q = mcDT l = length s = distance hi s M= molecular mass M = = - i u = speed F h0 s0 p = m = mass of sample x = position A n = number of moles R l = wavelength f = pV = nRT p = pressure 2 q = angle Q = heat transferred to a system d sin q = ml 3 K avg = k T T = temperature ml L 2 B xm U = internal energy d 3 RT 3k B T V = volume u rms = = M m u = velocity or speed urms = root-mean-square W = - pDV velocity Q = ncDT W = work done on a system y = height GEOMETRY AND TRIGONOMETRY DU = Q + W a = coefficient of linear expansion Rectangle A= area DU = ncV DT µ = mass of molecule A = bh C= circumference r = density Triangle V= volume W e = 1 S = surface area QH A = bh 2 b = base TH - TC Circle h = height ec = A = pr 2 l = length TH C = 2 pr w= width Parallelepiped r = radius ATOMIC AND NUCLEAR PHYSICS V = lwh E = hf = pc E = energy Cylinder f = frequency V = pr 2 l Kmax = hf − f S = 2 pr l + 2 pr 2 K = kinetic energy h m = mass Sphere l = p = momentum 4 V = pr 3 p 3 l = wavelength DE = ( Dm) c 2 f = work function S = 4 pr 2 Right Triangle a 2 + b2 = c2 c a a sin q = q 90 c b b cos q = c a tan q = b ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 MECHANICS ELECTRICITY AND MAGNETISM u = u 0 + at a = acceleration 1 q1 q 2 A = area F= 1 2 F = force 4p r2 B = magnetic field x = x0 + u 0 t + at 0 2 f = frequency C = capacitance 0 5 F u 2 = u 0 2 + 2a x - x 0 h = height E= d = distance q Ê F = Fnet = ma I = rotational inertia E = electric field J = impulse E • dA = Q e = emf dp F = K = kinetic energy 0 F = force dt I J = F dt = Dp k = l = spring constant length E=− dV dr I L = = current inductance p = mv L = angular momentum l = length ∑r 1 qi F fric mN m= mass V= n = number of loops of wire per 4p 0 W = IF dr N = P = normal force power i 1 i q1 q 2 P = power unit length 1 UE = qV = K = mu 2 p = momentum 4p 0 r Q= charge 2 r = radius or distance q = point charge dW Q P = r = position vector C= R = resistance dt T = period V r = distance P = F v k A t = time C= 0 t = time DU g = mgh U= potential energy d U= potential or stored energy u 2 = w2r u = velocity or speed C p = ∑ Ci V = electric potential ac = W= work done on a system i u = velocity or speed r t=rF x = position 1 =∑ 1 r = resistivity Ê t = t net = Ia m= coefficient of friction Cs i Ci fm = magnetic flux I I = r 2 dm = Ê mr 2 q = t = angle torque I= dQ k = dielectric constant rcm = Ê mr Ê m w= angular speed dt u = rw a = angular acceleration 1 1 Uc = QV = CV 2 L = r p = Iw 2 2 1 rl K = Iw 2 R= 2 A w = w0 + at V = IR q = q 0 + w0 t + 1 at 2 Rs = ∑ Ri 2 i Fs = - kx 1 1 =∑ 1 Rp i Ri Us = kx 2 2 2p 1 P = IV T = = w f FM = qv × B Ts = 2 p m B • d ø = m0 I Tp = 2 p k l I F = I dø × B g Bs = m0 nI FG = - Gm1m2 r2 $ r I fm = B • dA dfm UG = - Gm1m2 e=− r dt dI e = −L dt 1 2 U L = LI 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 GEOMETRY AND TRIGONOMETRY Rectangle A= area A = bh C= circumference Triangle V= volume 1 S = surface area A = bh 2 b = base Circle h = height A = pr 2 l= length C = 2 pr w= width Parallelepiped r = radius V = lwh Cylinder V = pr 2 l S = 2 prl + 2 pr 2 Sphere 4 V = pr 3 3 S = 4 pr 2 Right Triangle a 2 + b2 = c2 c a a sin q = q 90 c b b cos q = c a tan q = b CALCULUS df d f du = dx du dx d n dx 2 7 x = nx n -1 d x dx 2 7 e = ex d 1 (1n x) = dx x d (sin x) = cos x dx d (cos x) = - sin x dx Ixn dx = 1 n +1 n +1 x , n -1 Ie x dx = e x I dx x = 1n x I cos x dx = sin x I sin x dx = - cos x