Mitch Kwok Physics Equations and Notes Equations Equation 𝒗 = 𝒖 + 𝒂𝒕 𝟏 𝒔 = 𝒖𝒕 + 𝒂𝒕𝟐 𝟐 𝒗𝟐 = 𝒖𝟐 + 𝟐𝒂𝒔 𝒖+𝒗 𝒔= 𝒕 𝟐 𝑎 = 𝑔 sin 𝜃 ∆𝑣 𝑎= ∆𝑡 ⃗𝑭 = ⃗𝒅 𝐹1 𝐹2 𝐹3 = = sin 𝛼 sin 𝛽 sin 𝛾 𝟏 𝑬𝒌 = 𝒎𝒗𝟐 𝟐 𝑬𝒑 = 𝒎𝒈𝒉 1 𝐸𝑒𝑝 = 𝑘𝑥 2 𝑊 = 𝑓𝑠 cos 𝜃 = ∆𝐸 𝑝 = 𝑚𝑣 ∆(𝑚𝑣) 𝐹= 𝑡 𝑉 = 𝑉𝑝 sin 2𝜋𝑓𝑡 𝑄 𝐼= 𝑡 𝐸 𝑉= 𝑄 𝑉 = 𝐼𝑅 𝑛𝐴𝑙𝑒 𝐼= 𝑡 𝐼 𝑣= 𝑛𝐴𝑒 𝑬 𝑷 = = 𝑭𝒗 𝒕 𝑽𝟐 𝑷 = 𝑽𝑰 = 𝑹 𝒍 𝑹=𝝆 𝑨 𝑃𝑙𝑜𝑠𝑠 = 𝐸ℎ𝑒𝑎𝑡 = 𝐼 2 𝑅 𝜃 𝑥𝜃 − 𝑥0 = 100 𝑥100 − 𝑥0 𝑄 𝑇𝐻 − 𝑇𝐶 = 𝑘𝐴( ) 𝑡 𝑑 𝐸 𝐶= ∆𝑇 𝑬 𝒄= 𝒎∆𝑻 𝑚1 𝑐1 (∆𝑇1 ) = −𝑚2 𝑐2 (∆𝑇2 ) 𝑬 𝒍𝒇 = ∆𝒎 𝑽𝒑 𝑵𝒑 = 𝑽𝒔 𝑵𝒔 sin 𝑖 𝑣1 𝜆1 𝑛= = = sin 𝑟 𝑣2 𝜆2 Meaning Lami’s Theorem Eep = elastic potential energy W = work done (in Joule) F = impulse Peak Voltage for AC n = charge density, e = unit charge v = drift velocity Mechanical power Electrical power R = resistance, A = cross-sectional area, ρ = resistivity Thermometer k = thermal conductivity, Q = heat supplied, d = distance C = heat capacity (in J/K) c = specific heat capacity (in J/K kg) lf = latent heat N = number of turns n = refractive index 1 Mitch Kwok Physics Equations and Notes 𝑛1 ) 𝑛2 𝟏 𝟏 𝟏 + = 𝒖 𝒗 𝒇 ℎ𝐼 𝑣 𝑚= = ℎ𝑜 𝑢 𝑣 = 𝑓𝜆 𝑡 Φ = 2𝜋 𝑇 𝑐 = sin−1 ( 𝑣=√ Lens Formula m = magnification Phase 𝑇 𝜇 𝝀𝑫 𝒂 𝒅 𝐬𝐢𝐧 𝜽 = 𝒏𝝀 𝑃 𝐼= 4𝜋𝑟 2 𝐼2 𝑑𝐵 = 10 log10 ( ) 𝐼1 𝑣𝑦 = 𝑢 sin 𝜃 − 𝑔𝑡 1 𝑦 = 𝑢 sin 𝜃 𝑡 − 𝑔𝑡 2 2 𝑢𝑥 = 𝑣𝑥 = 𝑢 cos 𝜃 𝑚1 𝑦1 + 𝑚2 𝑦2 + ⋯ + 𝑚𝑛 𝑦𝑛 𝑦̅ = 𝑚1 + 𝑚2 + 𝑚𝑛 𝑚1 𝑥1 + 𝑚2 𝑥2 + ⋯ + 𝑚𝑛 𝑥𝑛 𝑥̅ = 𝑚1 + 𝑚2 + 𝑚𝑛 𝑠 = 𝑟𝜃𝑟 𝑣 = 𝑟𝜔 𝜔 𝑓= 2𝜋 2𝜋 𝑇= 𝜔 𝒗𝟐 𝒂= = 𝒓𝝎𝟐 𝒓 𝑚𝑣 2 𝐹𝑐 = 𝑟 𝑴𝒎 𝑭=𝑮 𝟐 𝒓 𝐺𝑀 𝑔= 2 𝑟 2 4𝜋 𝑇2 = 𝑟3 𝐺𝑀 𝐹 Fcos 𝜃 𝑝= = 𝐴 𝐴 𝑚𝑔 𝑝= = 𝜌ℎ𝑔 𝐴 𝑝1 𝑉1 = 𝑝2 𝑉2 𝑉1 𝑉2 = 𝑇1 𝑇2 𝑃1 𝑃2 = 𝑇1 𝑇2 𝑃1 𝑉1 𝑃2 𝑉2 = 𝑇1 𝑇2 𝒑𝑽 = 𝒏𝑹𝑻 𝚫𝒚 = 𝒑𝑽 = c = critical angle 𝑵𝒎𝒄𝟐 ∆y = bright fringe separation, D = distance a = slit separation d = slit separation, n = order of bright fringe I = intensity I0 = 10-12 Wm-2 Projectile Motion Centre of Gravity s = angular displacement v = tangential velocity, ω = angular velocity f = frequency T= period a= acceleration Fc = centripetal force F = gravitational force g = gravitational acceleration p = pressure ρ = density, h = depth Boyle’s Law (T is constant) Charle’s Law (p is constant) Pressure Law (V is constant) General Gas Law Ideal Gas Law (macroscopic), n = number of mole (Microscopic) p = ideal gas pressure, m = mass of one molecule, c = speed of molecules, N = number of molecules 2 Mitch Kwok Physics Equations and Notes 1 2 𝜌𝑐 3 3 𝐸𝑘 = 𝑁𝑅𝑇 2 𝟑 𝑹 𝐀𝐯𝐞𝐫𝐚𝐠𝐞 𝑬𝒌 = 𝑻 𝟐 𝑵𝑨 𝑸𝒒 𝑭 = 𝒒𝑬 = 𝟒𝝅𝜺𝒓𝟐 𝑄 𝐸= 4𝜋𝜀𝑟 2 𝐹 𝐸= 𝑄 𝑽 𝑬= 𝒅 𝑄 𝜎= = 𝜀𝐸 4𝜋𝑎2 𝐸𝑒 = 𝑊 = 𝑄𝑉 𝐹 𝐵 = 𝜇𝐻 = 𝐼𝑙 𝜇 = 𝜇0 𝜇𝑟 𝑭 = 𝑩𝑰𝒍 𝐬𝐢𝐧 𝜽 = 𝑩𝒒𝒗 𝐬𝐢𝐧 𝜽 𝑝= 𝑓 = 𝐵𝑒𝑣 sin 𝜃 𝐹 = 𝑁𝑓 = 𝑁𝐵𝑒𝑣𝑠𝑖𝑛𝜃 𝝁𝑰 𝑩= 𝟐𝝅𝒓 𝝁𝟎 𝑰𝑵 𝑩= 𝟐𝒓 𝜇0 𝐼𝑁 𝐵= 𝑙 𝐵 = 𝜇0 𝑛𝐼 𝜇0 𝑛𝐼 𝐵= 2 𝑚𝑔 𝐵= 𝐼𝑙 𝜇0 𝐼1 𝐼2 𝑙 𝐹= 2𝜋𝑎 𝐶 = 𝑁𝐵𝐴𝐼 sin 𝜃 𝐶 = 𝑁𝐵𝐴𝐼 𝜏 = 𝑐𝜃 𝑐𝜃 𝑁𝐵𝐴 𝜃 𝑁𝐵𝐴 = 𝐼 𝑐 Δ𝜙 𝜀= Δ𝑡 𝚫(𝑵𝝓) 𝜺= 𝚫𝒕 𝜙 = 𝐵𝐴 cos 𝜃 𝜀 = 𝐵𝑙𝑣 𝜀 = 𝐵𝜋𝑟 2 𝑓 𝐼= 𝜀 = 𝑁𝐵𝐴𝜔 sin 𝜔𝑡 𝑉𝑝 = 𝑁𝐵𝐴𝜔 (Microscopic) ρ = ideal gas density (Microscopic) T = ideal gas temperature NA = Avogadro’s Number, 𝑅 𝑁𝐴 = Boltzmann’s Constant Electric Force (in Newtons) E = electric field intensity (in Vm-1) For parallel charged plates, V = voltage, d = distance σ = charge density for spherical conductor, a = radius B = magnetic flux density (in T or Wb/m2), μ = permeability, H = magnetic field, l = length μ0 = permeability of free space, μr = relative permeability l = length of wire affected, θ = angle between B and I, v = speed of charges f = magnetic force, e = charge of an eN = number of eWire of ꚙ length, r = distance from measuring position to the wire Circular coil with N turns Solenoid with N turns If l can’t be measured, n = number of turns per unit length At the end of a long solenoid Current Balance experiment Parallel wires with same current direction, a = separation C = couple formed, A = area of the coil, θ = angle between I and the perpendicular of the coil DC practical motor or Moving Coil Galvanometer τ = opposite torque given by the hair spring in a Moving Coil Galvanometer, c = torsion constant/coefficient θ = angle that the pointer stops at (couple and torque are equal) Sensitivity of Galvanometer Faraday’s Law, ε = induced emf, φ = magnetic flux N = number of turns of the coil φ = magnetic flux (in Wb) l = length, v = velocity Spinning metal disc, ε = emf between the rim and the edge r = radius of disc, f = spinning frequency Rotating coil, ω = angular velocity 3 Mitch Kwok Physics Equations and Notes 𝜀𝑝 𝑁𝐴𝜔′ 1 𝑒𝑉 = 𝑚𝑣 2 2 𝐵0 = 2𝑒𝑉 𝑣=√ 𝑚 𝑚𝑣 𝑟= 𝑒𝐵 𝑒 𝐸2 = 𝑚 2𝑉𝐵2 𝑒 𝑉 = 2 2 𝑚 2𝑑 𝐵 𝑵 = 𝑵𝟎 𝒆−𝒌𝒕 𝒌= 𝒍𝒏𝟐 𝒕𝟏 𝟐 1 1 1 𝑁 = 𝑁0 ( )𝑡2 2 𝐴 = 𝐴0 𝑒 −𝑘𝑡 𝑨𝟎 = 𝒌𝑵𝟎 𝐻 = 𝐷𝑄 Search coil, εp = peak voltage, ω = angular frequency of the varying flux density, A = area e = charge of an e-, V = voltage r = radius of circular motion In an area with both e and m field when the path of the e𝑒 is not bent, = charge-mass ratio 𝑚 If voltage is the same Decay Law, N = number of nuclei, N0 = initial number of nuclei, k = decay constant, t = time t½ = half life Decay Law Activity (rate of decay) A0 = Initial activity H = dose equivalent (in Sv), D = doses absorbed, Q=quality factor 𝑬 = 𝒎𝒄𝟐 𝑐 𝐸 = ℎ𝑓 = ℎ 𝜆 𝑐 𝜙=ℎ 𝜆0 𝟏 𝒉𝒇 − 𝒉𝒇𝟎 = 𝒎𝒗𝟐 = 𝒆𝑽𝒔 𝟐 𝒎𝒂𝒙 𝑛ℎ𝑓 𝐼= 𝐴𝑡 ℎ𝑓 = Δ𝐸 = 𝐸𝐻 − 𝐸𝐿 𝟏 𝒎𝒆 𝒆 𝟒 𝑬𝒏 = − 𝟐 ( 𝟐 𝟐 ) 𝒏 𝟖𝒉 𝜺 𝟏 𝑬𝒏𝑯𝒚𝒅𝒓𝒐𝒈𝒆𝒏 = − 𝟐 𝟏𝟑. 𝟔 𝒏 𝐸𝐼𝑜𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 𝐸∞ − 𝐸1 1 1 𝐸𝐸𝑥 = 13.6 ( − ) 𝑒𝑉 𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 2 𝐸𝑓𝑖𝑛𝑎𝑙 2 1 1 𝐸𝑅𝑒𝑙 = 13.6 ( ) 𝑒𝑉 2− 𝐸𝑓𝑖𝑛𝑎𝑙 𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 2 𝒉 𝝀= 𝒑 ℎ 𝜆= √2𝑚𝑒 𝑒𝑉 ℎ 2𝜋𝑟𝑛 = 𝑛 𝑚𝑒 𝑣 ℎ 𝑚𝑒 𝑣𝑟𝑛 = 𝑛 2𝜋 𝑑 = 𝑟1 𝜃1 𝟏. 𝟐𝟐𝝀 𝜽≈ 𝒅 1.22𝜆 𝑠≈𝑟 𝑑 E = energy of radiation, f = frequency, h = Planck’s constant φ = work function, 𝜆0 = threshold frequency Photoelectric equation (for one e- only) I = intensity, n = number of photons n = energy level Eꚙ = 0 Excitation energy Energy of photons released De Broglie formula, p = momentum, λ = de Broglie wavelength Quantization, n = principal quantum number, r = radius of n Angular momentum, n = quantum number of the shell d = separation of 2 points, r1 = distance In an optical microscope, s = separation of 2 points, r = distance, d = aperture size 4 Mitch Kwok 𝑠 ≈ 0.61𝜆 𝝓 𝐜𝐨𝐬 𝜽 𝑬= 𝑨 𝜙 𝐸= 4𝜋𝑟 2 𝜙 cos 𝜃 𝐸= 4𝜋𝑟 2 luminous flux Efficacy = power output 𝑄𝐻 = 𝑄𝐶 + 𝑊 𝑄𝐶 Cooling capacity = 𝑡 𝑄𝐶 COP = 𝑄𝐻 − 𝑄𝐶 𝑸 𝑻𝑯 − 𝑻𝑪 = 𝒌𝑨( ) 𝒕 𝒅 𝒌 𝑼= 𝒅 𝑄 = 𝑈𝐴(𝑇𝐻 − 𝑇𝐶 ) 𝑡 𝑄𝑐 𝑄𝑟 + 𝑡 𝑂𝑇𝑇𝑉 = 𝑡 𝐴 𝟏 𝑷𝒎𝒂𝒙 = 𝝆𝑨𝒗𝟑 𝟐 Physics Equations and Notes In an optical microscope E = illuminance (in lux), φ = luminous flux (in lm) Lambert’s Cosine Law, θ = angle between surface and source In lmW-1 W = energy used by heat pump Q = heat removed QH-QC = energy supplied U = U-value, or thermal transmittance Qc = heat transfer by conduction, Qr = heat transfer by radiation Wind turbines, A = area swept, ρ = air density, v = wind speed 5 Mitch Kwok Physics Equations and Notes Notes Electricity RMS of sine graph = 𝑉𝑝 √2 EM Wave Wavelength 10-12 10-9 10-8 4×10-7 to 7×10-7 10-4 10-2 103 Sound Gas Name Gamma ray X-ray Ultraviolet Visible light Infrared Microwave Radio wave Frequency 1020 1017 1016 1015 1012 1010 105 Longitudinal mechanical wave Fastest in air and slowest in solids Fastest in high temperature and density 20 to 20,000 Hz can be heard by human ears Ideal Gas o Intermolecular force = 0 o Potential energy between molecules = 0 Kinetic theory o Intermolecular forces are negligible except for during collisions o Volume of molecules are negligible o Time taken for collision is negligible o Molecules move with uniform velocity except for during collisions Photoelectric EM radiation is proportional to the frequency of photoelectrons emitted KEmax is proportional to frequency, but not intensity of EM radiation Rutherford’s Model Most of the volume is space Positive charge and mass are concentrated at the nucleus Electrons orbit the nucleus Limitations o Electrons will lose energy through circular motion and the atom would collapse o Due to different accelerations and radii of electrons, there should be different frequencies of EM waves Bohr’s Model Electrons orbit the nucleus (obeying circular motion and Coulomb’s Law) Electrons move in stationary, discrete and quantized orbits of defined energy ℎ Angular momentum of electrons (quantized) are multiples of 2𝜋 6
