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# Physics Equations

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### Physics Equations

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