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Important Equations in Physics (A2) 1 Unit 1: Non-uniform Acceleration (Topic 7 and 14) Base units Length Mass Time meters Tera T 1012 Giga G 109 Kilograms Mega M 106 Multiples of units 3 Radian : Angle subtended by an arc equal to the length of radius Radian and degree 2 = 360 1 = 57.3 Angular displacement, θ in radians Δ Angular speed, ω in = radians/seconds Δ Centripetal Force, Fc = 4 5 6 7 8 Centripetal acceleration 9 10 11 12 13 Oscillations Period T Frequency f Displacement x Amplitude xo Simple Harmonic Motion 14 15 16 Simple Harmonic Motion Angular frequency Restoring force, 17 Simple harmonic motion Equations seconds Kilo K 103 2 Temp kelvin(K) Deci d 10-1 centi c 10-2 milli m 10-3 ℎ = Current ampere (A) micro µ 10-6 ℎ = × = = = = Time taken for one complete oscillation. Unit seconds Number of oscillations per second. Unit oscillations per second or hertz or Hz The distance from the equilibrium position at any time t. Unit meters, vector qty The maximum displacement from the mean position. Unit meters, scalar qty a) motion about a fixed point, b) acceleration is proportional to displacement and directed towards a fixed point, c) direction of acceleration is opposite to displacement. a, acceleration; ω, angular frequency; x, displacement =− =2 f is frequency of oscillations The resultant force acting on an oscillating particle that cause acceleration a. =− at t=0 and x=0 at t=0 and x=xo = sin = cos = cos =− sin = = =± ( =− = − sin ( − ) =± Total energy for SHM 19 Time period for Simple pendulum and mass on a helical spring ) 20 21 22 Free oscillations Damped oscillations Resonance − cos ( − ) ) = = =2 ( =− = = 18 = 180 = × 180 s is the arc length in meters r is the radius of a circle in meters is called omega, is a vector, direction clockwise or anticlockwise unit newtons, N, always directed towards the centre of the circle of radius r unit m/s2 or rad/s2 direction always towards the centre of the circle = = luminous Amount of intensity substance candela (Cd) mole nano pico femto atto n p f a 10-9 10-12 10-15 10-18 + = =2 l is the length of the pendulum m is the mass and k is the spring constant When the only force acting on a particle is external restoring force. When frictional and resistive force reduce the amplitude (energy) of the oscillation When driving freq. of the osc. is equal to natural frequency gives max amplitude Important Equations for A2 Physics - 9702 Prepared by Faisal Jaffer - 1 Unit 2: Thermal Physics (Topic 11, 12, 13) 1 Mole: amount of substance, n eg 1 mole carbon=12g, 1 mole of oxygen=16g, 1 mole of water=18g 2 Avogadro constant, NA Constant number of molecules or atoms in 1 mole=6.023×1023 particles 3 Brownian motion Random, jerky, haphazard, zigzag motion of molecules in liquid or gas 4 Absolute Temperature, K Temperature in kelvin scale T/K=θ/oC+237.15 5 Ideal gas equation pV=nRT P=pressure, V=volume, T=temp in Kelvin, n number of moles, R=universal gas constant per mole=8.3Jmole-1K-1. 6 Ideal Gas - gas that obeys ideal gas equation at all pressures, volumes, temperatures, - molecules do not exert forces on each other when collide, - the collision between the molecules is perfectly elastic 7 Kinetic theory of ideal gas - Matter is made of tiny particles called atoms or molecules, - These particles are in constant, random motion, - Particles collide with each other and collision is perfectly elastic, - Particles apply no force on each other when collide, - Motion of particles is greater in gas, less in liquid and least in solids, - Volume of particles in gas is negligible compare to the volume of gas. 〈 〉 or = 〈 〉 8 Kinetic theory of ideal gas = N is the total number of molecules, m is the mass of a molecule, p the pressure, V the volume of container, 〈 〉 the average of square of the velocities of molecules, = , ℎ . 9 Other gas equations R=universal gas constant (per mole) =8.3Jmole-1K-1 = k=boltzmann constant (per molecule)=1.38×10-23JK-1 = = , Avogadro no. 6.023×1023molecules/mole = 10 Average of 〈 〉 molecules T, the temperature in kelvin, k, the boltzmann constant 〈 〉= 11 Heat and temperature 12 Internal energy ΔU 13 Law of thermodynamics 14 Thermal equilibrium 15 Physical properties of matter when heated 16 Thermocouple thermometer (junction between copper and iron wire) 17 Specific heat capacity: ..amount of heat required to raised the temperature of unit mass of a substance to one degree 18 Thermal capacity, C unit J/oC 19 Specific latent heat: ..amount of heat require to change the state of unit mass of matter without increase of temperature Important Equations for A2 Physics - 9702 Heat is a form of energy Temperature is the degree of hotness of an measured in joules object measure in oC or K In ideal gas, it is the sum of kinetic In real gas, it is the sum of kinetic and energies of all molecules potential energies of all molecules The increase in internal energy (ΔU) of a system is equal to the sum of heat energy added to the system and the work done on it. ∆ = + Q is the heat energy and W(=pΔV), is the work done on the system When all sections of a system are at same temperature - most materials expand upon heating, eg mercury in glass thermometer - resistance of metals increases when the temperature increases, eg thermocouple thermometer a) wide range (-200oC to 1500oC) b) can store data electronically c) small size easy to manage d) record very rapid change of temperature e ) can measure the temperature of small objects ∆ c, the specific heat capacity, Jkg-1oC-1 = m, the mass of an object, kg ×∆ Δθ, the change in temperature, oC × ΔQ, amount of heat energy, J = P, the power of electrical heater, W ×∆ t, ON time for electrical heater, s ∆ ..heat required to increase the =∆ or = × temperature of a whole body ..of fusion → from solid to liquid ..of vaporization→ from liquid to gas × × = = = = unit J/kg Always > unit J/kg for the same substance Prepared by Faisal Jaffer - 2 Unit 3: Force fields (topic from syllabus 8, 17, 18, 21, 22) Gravitational field 1 Newton’s law of Every two objects attract each other with force directly proportional to their gravitation masses and inversely proportional to the square of the distance between them × 2 Gravitational force F the force in newton, m1 & m2 masses, G = between two masses universal force constant 6.67×10-11 Nm2kg-2 × 3 Earth’s Gravitational Me the mass of earth, R the radius of earth = = force on mass m 4 Gravitational field Force per unit mass placed at a point in a = gravitational field=9.81Nkg-1 strength, g × 5 Gravitational potential work done against the gravity on bringing the =− = energy, Ep mass to distance r above the surface of the earth (r=R+Δh) 6 Gravitational potential Potential energy per unit mass = =− ϕ 7 Geostationary orbit The square of the period is proportional to the 4 = cube of the radius of orbit Electric field 1 × 8 Coulomb’s law of q1, q2 charged objects in coulombs, r the distance = electrostatic between the charged objects, ϵo the permittivity of 4 free space=8.85×10-12C2N-1m-2 1⁄4 =9×109C-2 Nm2 1 9 Electric field intensity, - force on a unit charge q at any point around = = E, due to charge Q another charge Q 4 - out from positive end to negative charge 10 Electric field intensity, V the potential difference between the plates = E, between the two d the distance between the plates charged plates E is uniform between the plates, unit is Vm-1 11 Electric potential, V .. work done in bringing the point charge from = infinity to a point r in an electric field 4 Capacitance 12 Capacitance, C ratio of charge (Q) stored to potential diff.(V) = between conductor, unit Farad, mF and µF 13 Electric pot. energy - Capacitor is use to store charges or energy, = = = stored in a capacitor - has two plates and insulator in between 14 Factors affecting A the area of parallel plates, d the distance = capacitance between them, ϵo permittivity of free space, ϵr relative permittivity of dielectric 15 Relative permittivity ϵr Capacitance with dielectric divided by capacitance with vacuum, no units 16 Capacitors connected .. parallel = + .. series = + in... Magnetic fields 17 Magnetic field Force of field around magnets or current carrying conductor 18 Magnetic flux density B the magnetic field strength or force per unit length of conductor, unit tesla (T) 19 Magnetic flux ϕ Product of magnetic flux density (B) and area (A) normal to the magnetic field lines, unit weber (Wb) or tesla meter square (T m2) = 20 Force (F) in magnetic ..on current carrying conductor ..on moving charge q with speed v field = = 21 Specific charge of The ratio of charge to mass of an electron ⁄ = electron e/m 22 Faraday`s law of EM Emf produce is directly proportional to rate of change of magnetic flux linkage induction 23 Hall probe Use to find amount of magnetic field by creating hall voltage VH in a conductor Important Equations for A2 Physics - 9702 Prepared by Faisal Jaffer - 3 Unit 5 Modern Physics (Topics from syllabus 25, 26 and 27) Charges Particles 1 Photoelectric effect 2 3 Photoelectric effect: Properties Threshold freq fo 4 Max Plank Equation 5 Photon 6 Work function energy ϕ Photoelectric equation 7 Emission of electrons from metals when e.m. radiations fall on it. Proof of light as particles that is particle strikes particle emits a) instantaneous b) only happen if the freq is above minimum level c) each metal have its own freq d) rate of electrons emits is proportional to intensity The minimum freq of wave required to emit the electrons from the metals, each metal have its own threshold frequency. E the energy, f the freq and h the = ℎ Planks constant= 6.63×10-34Js Light as packets and energy of these packets are quantized, only on certain fixed levels. The minimum amount of energy require ϕ work function energy in J, fo the threshold freq, h planks constant for electron to escape, = ℎ =ℎ = + =ℎ =ℎ + p is momentum of the particle ℎ de Broglie wavelength, λ = Equation of wave particle duality 9 Electromagnetic spectra Continuous spectra: spectrum of Line spectra: spectrum of only few all colours and wavelengths colours and wavelengths shown as lines 10 Quantization of energy When electron jump from: ∆ = − =ℎ levels in atomic orbits lower to higher energy state → absorb energy higher to lower energy state → emit energy Nuclear Physics 11 Atomic mass unit,1u 1u=1.66×1027kg Equal to one-twelfth of the mass of carbon-12 atom 12 Mass deficit Difference between the total mass of separate nucleons and combine nucleus 13 Mass – Energy Equation E is the energy, m the mass and c the speed of light = 1 = 931 14 eV the unit of energy 1eV=1.6×10-19J 1MeV=1.6×10-13J 15 Binding energy Energy equivalence of mass deficit, energy require to separate the nucleons 16 Binding energy per Total energy require to separate the nucleons divided by the number of nucleon nucleons (study the graph on page no 369 of AS Physics by Chris Mee.....) 17 Nuclear fusion Smaller nuclei combine together to form larger nuclei, require high temperature and pressure 18 Nuclear fission Heavy nuclei bombarded with neutrons, split into smaller nuclei, release energy Quantum Physics 19 Photoelectric effect Emission of electrons from metals when e.m. radiations fall on it. Proof of light as particles 20 Photoelectric effect: a) instantaneous b) only happen if the freq is above minimum level c) each Properties metal have its own freq d) rate of electrons emits is proportional to intensity 21 Threshold freq fo The minimum freq of wave required to emit the electrons from the metals, each metal have its own threshold frequency. 22 Max Plank Equation E the energy, f the freq and h the = ℎ Planks constant= 6.63×10-34Js 23 Photon Light as packets and energy of these packets are quantized . 24 Work function energy The minimum amount of energy require ϕ work function energy in J, fo the ϕ for electron to escape, = ℎ threshold freq, h planks constant 25 Photoelectric equation =ℎ = + 8 =ℎ =ℎ Important Equations for A2 Physics - 9702 + Prepared by Faisal Jaffer - 4 26 27 28 de Broglie wavelength,λ Equation of wave/ particle duality Electromagnetic spectra Quantization of energy levels in atomic orbits Important Equations for A2 Physics - 9702 = ℎ Continuous spectra: spectrum of all colours and wavelengths ∆ = − =ℎ p is momentum of the particle Line spectra: spectrum of only few colours and wavelengths shown as lines When electron jump from: lower to higher energy state → absorb energy higher to lower energy state → emit energy Prepared by Faisal Jaffer - 5