Important Equations in A Level Physics CIE P2: Planning, analysis and evaluation 1 Choice of axes for straight-line graphs Relationship Graph y = mx+c y against x ln y against ln x lg y against lg x y = axn 3 4 m c n ln a lg a Because... ln y = n ln x + ln a lg y = kx + ln a Always add uncertainties, never subtract. Where quantities are: • Added or subtracted, then add absolute uncertainties; • Multiplied or divided, then add percentage uncertainties. y = aekx 2 Intercept on yaxis Gradient Combining uncertainties Uncertainties and logarithms Error in gradient ln y against x k ln a logarithm likely value - logarithm smallest/largest value error = (gradient of the best fit line) – (gradient of worst acceptable line) Circular Motion (Unit 7 syllabus) 5 6 7 Angle in radians π= πππππ‘β ππ πππ π = πππππ’π π To convert from degrees to radians, multiply by To convert from radians to degrees, multiply by 8 Angular velocity 9 Relating velocity and angular velocity 10 Centripetal acceleration 11 Centripetal force π= 34 567 567 ;<=>?;@ ABCD?;EFGF<H HBGF H;IF< 34 = or or βK βH 4 897 897 4 = 34 L =2ππ speed = angular velocity × radius βΉ π£ = ππ = 34@ L 3 π£ = π3 π π ππ£ 3 πΉ= = πππ3 π π= Gravitational Fields (Unit 8 syllabus) 12 Gravitational constant G 13 Newton’s law of gravitation 14 Gravitational field strength g 15 Gravitational potential 16 Gravitational potential energy πΊ = 6.67 × 10Z88 ππ3 πΎπZ3 πΊππ π3 πΉ πΊπ π= = 3 π π The gravitational potential at a point is the work done per unit mass in bringing a mass from the infinity to the point πΊπ π=− π πΊππ π. π. π. = − π πΉ= Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 – 1 17 18 π£3 = Orbital speed v ab @ π3 = Orbital period or π£ = 34@ L 3 4π π5 πΊπ Oscillations (Unit 13 syllabus) 8 19 Period Time (T) for a complete oscillation π = 20 Frequency Frequency (f) is the number of oscillations per unit time π = 21 Equations of s.h.m. π₯ = π₯7 sin ππ‘ or π₯ = π₯7 cos ππ‘ 22 Acceleration of an oscillator π = −π3 π₯ 23 Velocity of an oscillator or π£ = π£7 cos ππ‘ or π£ = ±π π₯73 − π₯ 3 24 Maximum velocity of an oscillator π£ = ππ₯7 25 Kinetic energy 26 Potential energy 27 Phase difference e 1 πΈ = ππ3 (π₯73 − π₯ 3 ) 2 1 πΈ = ππ3 π₯ 3 2 π₯ π‘ ∅ = 2π ππ ∅ = 2π π π Communication (Unit 16 syllabus) 28 Attenuation 29 Attenuation per unit length 30 Signal to noise ratio 31 ππ’ππππ ππ ππ΅ = 10πππ wHHF<>;HBx< Ay zF<=H{ xe |;}?F (~G) 10πππ tu tv 8 tu z tv = 10πππ ππππππ πππ€ππ ππππ π πππ€ππ Thermal Physics (Unit 12 syllabus) The internal energy of a system is the sum of the random Internal Energy distribution of kinetic and potential energies of its atoms or molecules Δπ = π + π€ 32 First law of Thermodynamics 33 Specific Heat Capacity πΈ = ππβπ 34 Specific Latent Heat πΈ = ππΏ Ideal Gases (Unit 10 syllabus) 35 Boyle´s Law pV=constant or π8 π8 = π3 π3 Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 – 2 8 L 36 Ideal gas equation 37 Pressure 38 ππ = ππ π 1 ππ π 3 1 π= = ππ3 3 π 3 1 3ππ π πΈ= ππ3= (π = ) 2 2 πw Mean translational kinetic energy E of a particle of an ideal gas Coulomb’s Law (Unit 17 syllabus) 39 Œu Œv πΉ= Coulomb´s Law 40 Work done in moving a charge from the negative to the positive plate 41 Electric Field Strength πΈ= 42 Electric Potential π= •4Ε½• @ v π= Œ •4Ε½• @ v π 4ππ7 π πΈ= 43 Field Strength (uniform field) π π “ A Capacitance (Unit 18 syllabus) 44 Capacitance 45 Work done in charging a capacitor 46 Capacitors in parallel (all have same voltage) 47 Capacitors in series (all have same charge) 48 Capacitance of isolated bodies πΆ= π π 1 1 1 π3 π = ππ = πΆπ 3 = 2 2 2 πΆ πHxH;? = π8 + π3 + π5 + β― πΆHxH;? = πΆ8 + πΆ3 + πΆ5 + β― 1 πΆHxH;? Electronics (Unit 21 syllabus) = 1 1 1 + + +β― πΆ8 πΆ3 πΆ5 πΆ = 4ππ7 π π e πx>H =− πB< π B< πx>H π 8 πΊ= =1+ πB< π 3 + If V is slightly greater in magnitude than V-, then Vout will have a magnitude equal to the positive power supply voltage. + If V is slightly smaller in magnitude than V-, then Vout will have a magnitude equal to the negative power supply voltage. πΊ= 49 Inverting Amplifier 50 Non-inverting Amplifier 51 The op-amp as a comparator Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 – 3 52 53 54 55 Magnetic Fields (Unit 22 syllabus) Magnetic Flux Density for a uniform magnetic field Magnetic Force on a current-carrying conductor Magnetic flux density for charged particles Charged particles (Unit 22 syllabus) Magnetic force on a moving particle at right angles to a magnetic field 56 Electron traveling in a uniform magnetic field 57 Velocity of an undeflected charged particle in a region where electric and magnetic fields are at right angles 58 Hall Voltage 59 Charge-to-mass ratio 60 Kinetic energy of electrons leaving the anode in a deflection tube π΅= πΉ πΌπΏ πΉ = π΅πΌπΏ sin π π΅= ππ£ ππ πΉ = π΅ππ£ πF π£ 3 = π΅ππ£ π πΈ π£= π΅ π΅πΌ π— = ππ‘π π 2πE; = 3 3 πF π π΅ 1 ππ£ 3 = ππE; 2 Electromagnetic induction (Unit 23 syllabus) 61 Magnetic flux F through area A 62 Faraday’s law 63 Magnetic flux linkage ππ· = ππ΅π΄ cos π 64 Motional e.m.f π = π΅ππ£ π· = π΅π΄ πΈ= β(ππ·) βπ‘ Electromagnetic induction (Unit 24 syllabus) 65 Sinusoidal alternating current πΌ = πΌ7 sin ππ‘ 66 Sinusoidal alternating e.m.f. π = π7 sin ππ‘ 67 Root-mean-square of an alternating current πΌ@GC = πΌ7 / 2 68 Transformers πC π› = πD πD πΌD πD = πΌC πC Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 – 4 Quantum Physics (Unit 25 syllabus) πΈ = βπ or πΈ = {E 69 Energy of a photon 70 Kinetic energy of a particle of charge e accelerated through a voltage V 1 ππ = ππ£ 3 2 71 Einstein’s photoelectric equation βπ = π· + π. π.G;• 72 De Broigle wavelength π= 73 Difference in energy between two levels when a photon is either emitted or absolved βπΈ = πΈ8 − πΈ3 = βπ = œ β ππ£ βπ π Nuclear Physics (Unit 26 syllabus) 74 Einstein energy-mass equation 75 Activity of a radioactive sample 76 Exponential decrease of a quantity (A/R/N) 77 Half-life πΈ = ππ 3 βπ = −ππ βπ‘ π΄= π₯ = π₯7 π (ZœH) π‘8 3 = ln 2 0.693 = π π Medical Imaging (Unit 22 and 25 syllabus) ππ β 78 Maximum X-ray frequency πG;• = 79 Attenuation of X-rays as they pass a uniform material πΌ = πΌ7 π Z 80 Half thickness 81 Acoustic impedance of a material 82 Fraction of the intensity of an ultrasound wave reflected at a boundary 83 Thickness of bone πβππππππ π ππ ππππ = 84 Lamour frequency 85 Frequency f0 of the processing nuclei π₯8 3 = • ln 2 π π = ππ£ πΌH π3 − π8 = πΌ7 π3 + π8 3 3 π3 − π8 = π3 + π8 3 πππ π‘ππππ π‘πππ£πππππ ππ¦ π’ππ‘πππ ππ’ππ πΔπ‘ = 2 2 π7 = πΎπ΅7 π7 = ππ΅7 2π Prepared by Renato Martins – renato.martins@civ.pt – v 2.2/2017 – 5