A-level Physics data and formulae
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1 A-level Physics data and formulae For use in exams from the June 07 Series onwards DATA - FUNDAMENTAL CONSTANTS AND VALUES Quantity Symbol Value Units speed of light in vacuo c m s permeability of free space µ 0 4π 0 7 H m permittivity of free space ε F m magnitude of the charge of electron e C the Planck constant h J s gravitational constant G N m kg the Avogadro constant N A mol molar gas constant R 8.3 J K mol the Boltzmann constant k J K the Stefan constant σ W m K 4 the Wien constant α m K electron rest mass (equivalent to u) electron charge/mass ratio proton rest mass (equivalent to.0078 u) proton charge/mass ratio neutron rest mass (equivalent to u) m e kg e m e.76 0 C kg m p.67(3) 0 7 kg e m p C kg m n.67(5) 0 7 kg gravitational field strength g 9.8 N kg acceleration due to gravity g 9.8 m s atomic mass unit (u is equivalent to 93.5 MeV) u kg ALGEBRAIC EQUATION GEOMETRICAL EQUATIONS quadratic equation x = b ± b 4ac a arc length circumference of circle = rθ = πr ASTRONOMICAL DATA area of circle = πr Body Mass/kg Mean radius/m curved surface area of cylinder = πrh Sun area of sphere = 4πr Earth volume of sphere = 3 4 πr 3 Version.
2 Particle Physics Class Name Symbol Rest energy/mev photon photon γ 0 lepton neutrino v e 0 v µ 0 electron e ± muon µ ± mesons π meson π ± π K meson K ± K baryons proton p Waves wave speed c = ff period f = T first harmonic fringe spacing f = l T μ w = λd s diffraction grating d sin θ = nn refractive index of a substance s, n = c c s for two different substances of refractive indices n and n, law of refraction n sin θ = n sin θ critical angle sin θ c = n n for n > n Mechanics neutron n Properties of quarks antiquarks have opposite signs Type Charge Baryon number u + 3 e + 3 d 3 e + 3 s 3 e + 3 Properties of Leptons Strangeness 0 0 Lepton number Particles: e, ν e ; µ, ν µ + Antiparticles: e +, ν e, µ +, ν µ Photons and energy levels moments velocity and acceleration equations of motion force force impulse work, energy and power Materials density ρ = m V moment = FF v = s v = u + aa v = u + aa F = mm F = (mm) F Δt = Δ(mm) W = F s cos θ a = v u + v s = t s = uu + aa E k = m v ΔE p = mmδh P = W, P = FF uuuuuu oooooo ppppp eeeeeeeeee = iiiii ppppp Hooke s law F = k ΔL photon energy E = hf = hc /λ photoelectricity hf = φ + E k (max) energy levels hf = E E de Broglie wavelength λ = h p = h mm ttttttt ssssss Young modulus = ttttttt ssssss energy stored E = FΔL tensile stress = F A tensile strain = L L Version.
3 AQA GCE PHYSICS DATA AND FORMULAE Electricity Gravitational fields current and pd I = Q V = W Q R = V I force between two masses F = Gm m r resistivity ρ = RR L gravitational field strength g = F m resistors in series resistors in parallel R T = R + R + R 3 + R T = R + R + R 3 + magnitude of gravitational field strength in a radial field g = GG r ΔW = mδv power P = VV = I R = emf Circular motion magnitude of angular speed centripetal acceleration centripetal force ε = E Q Simple harmonic motion acceleration displacement ω = v r ω = ππ a = v r F = mm r V R ε = I(R + r) = ω r a = ω x = mω r x = A ccc (ω t) speed v = ± ω (A x ) gravitational potential Electric fields and capacitors force between two point charges force on a charge field strength for a uniform field field strength for a radial field electric potential F = F = EE V = GG r g = ΔV Δr Q Q 4πε 0 r E = V d ΔW = QΔV E = Q 4πε 0 r V = Q 4πε 0 r E = ΔV Δr maximum speed maximum acceleration for a mass-spring system for a simple pendulum v mmm = ω A a mmm = ω A T = π m k T = π l g capacitance C = Q V C = Aε 0ε r d capacitor energy stored E = QQ = CV = Q C capacitor charging Q = Q 0 ( e t/rr ) Thermal physics energy to change temperature Q = mmδθ decay of charge time constant Q = Q 0 e t/rr RR energy to change state Q = m l gas law pp = nnn pp = NNN kinetic theory model pp = 3 N m (c rms) kinetic energy of gas molecule m (c rms) = 3 3RR kk = N A Version. 3
4 Magnetic fields force on a current force on a moving charge magnetic flux magnetic flux linkage magnitude of induced emf emf induced in a rotating coil Ф = BB NФ = BBB cos θ ε = N ΔФ Δt alternating current I rms = I 0 transformer equations Nuclear physics NФ = BBB cos θ ε = BBBω sin ω t N s N p = V s V p V rms = V 0 eeeeeeeeee = I sv s I p V p the inverse square law for γ radiation I = k x radioactive decay activity ΔN Δt = λ N, N = N oe λt A = λλ half-life T ½ = ln λ nuclear radius R = R 0 A /3 energy-mass equation E = mm OPTIONS Astrophysics astronomical unit =.50 0 m light year = m parsec = 0665 AU = m = 3.6 light year Hubble constant, H = 65 km s Mpc M = aaaaa sssssssss bb iiiii aa eee aaaaa sssssssss bb oooooo aa uuuuuuu eee in normal adjustment M = f 0 f e Rayleigh criterion θ λ D magnitude equation m M = 5 log d 0 Wien s law Stefan s law P = σσt 4 Schwarzschild radius Doppler shift for v << c red shift Hubble s law Medical physics λ max T = m K R s GM c Δf f = Δλ λ z = v c v = HH = v c lens equations P = f threshold of hearing m = v u f = u + v I 0 =.0 0 W m intensity level iiiiiiiii lllll = 0 log I I 0 absorption I = I 0 e μμ μ m = μ ρ ultrasound imaging half-lives Z = p c I r = Z Z I i Z + Z T E = T B + T P 4 Version.
5 AQA GCE PHYSICS DATA AND FORMULAE Engineering physics moment of inertia I = Σmm angular kinetic energy equations of angular motion torque angular momentum angular impulse power thermodynamics adiabatic change isothermal change heat engines efficiency = maximum theoretical efficiency = E k = Iω ω = ω + α t ω = ω + αα θ = ω t + αα θ = (ω + ω ) t T = I α T = F r aaaaaaa mmmmmmmm = Iω TΔt = Δ(II) W = TT P = Tω Q = ΔU + W W = pδv pp γ = constant pp = constant W = Q H Q C Q H Q H T H T C T H per cycle = area of loop input power = calorific value fuel flow rate indicated power = (aaaa oo p V llll) (nnnnnn oo cccccc ppp ssssss) (nnnnnn oo ccccccccc) output or brake power P = Tω friction power = iiiiiiiii ppppp bbbbb ppppp heat pumps and refrigerators refrigerator: CCC ref = Q C W = heat pump: CCC hp = Q H W = Q C Q H Q C Q H Q H Q C Turning points in physics electrons in fields Millikan s experiment Maxwell s formula c = special relativity t = Electronics resonant frequency Q-factor operational amplifiers: open loop inverting amplifier non-inverting amplifier summing amplifier difference amplifier F = ee d r = mm BB ½ mm = ee QQ d = mm F = 6ππππ μ 0 ε 0 λ = h p = t 0 h mmm v c l = l 0 v c E = m c = f 0 = π LL Q = f 0 f B m 0 c v c V out = A OL (V + V ) V out V in V out V in = R f R in = + R f R l V out = R f V R + V R + V 3 R 3 + V out = (V + V ) R f R l Bandwidth requirement: for AM bbbbbbbbh = f M for FM bbbbbbbbh = ( f + f M ) Version. Copyright 06 AQA and its licensors. All rights reserved. 5
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