Important Equations in Physics (A2) θ = s s is the arc length in meters in radians

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1 Impotant Equations in Physics (A2) Unit 1: Non-unifom Acceleation (Topic 7 and 14) 1 Base units Length metes Mass Kilogams Time seconds 2 Multiples of units Tea T Giga G 10 9 Mega M Radian : Angle subtended by an ac equal to the length of adius Kilo K 10 3 θ = Deci d 10-1 centi c 10-2 Temp kelvin(k) milli m 10-3 Cuent ampee (A) mico µ 10-6 nano n 10-9 luminous intensity candela (Cd) pico p Amount of substance mole femto f length of ac cicumfeence of the cicle = = s adius of cicle adius 4 Radian and degee 2π ad = ad = 57.3 adian = degee π 180 degee = ad 180 π 5 Angula displacement, θ θ = s s is the ac length in metes in adians is the adius of a cicle in metes 6 Angula speed, ω in adians/seconds ω = Δθ ω is called omega, is a vecto, diection v = ω Δt clockwise o anticlockwise 7 Centipetal Foce, F c F = mv F = mω unit newtons, N, always diected towads the cente of the cicle of adius 8 Centipetal acceleation a = v a = ω unit m/s 2 o ad/s 2 diection always towads the cente of the cicle Oscillations 9 Peiod T Time taken fo one complete oscillation. Unit seconds 10 Fequency f Numbe of oscillations pe second. Unit oscillations pe second o hetz o Hz 11 Displacement x The distance fom the equilibium position at any time t. Unit metes, vecto qty 12 Amplitude x o The maximum displacement fom the mean position. Unit metes, scala qty 13 Simple Hamonic Motion a) motion about a fixed point, b) acceleation is popotional to displacement and diected towads a fixed point, c) diection of acceleation is opposite to displacement. 14 Simple Hamonic Motion a = ω x a, acceleation; ω, angula fequency; x, displacement 15 Angula fequency ω = 2πf f is fequency of oscillations 16 Restoing foce, F The esultant foce acting on an oscillating paticle that cause acceleation a. F = mω x 17 Simple hamonic motion Equations at t=0 and x=0 x = x sin ωt v = x ω cos ωt v = x ω v = ±ω(x x ) a = x ω sin ωt E = mω (x x ) E = mω x at t=0 and x=x o x = x cos ωt v = x ω sin ωt v = x ω 18 Total enegy fo SHM E = E + E = mω x v = ±ω(x x ) a = x ω cos ωt E = mω (x x ) E = mω x 19 Time peiod fo Simple pendulum and mass on a helical sping T = 2π l g l is the length of the pendulum T = 2π m k m is the mass and k is the sping constant 20 Fee oscillations When the only foce acting on a paticle is extenal estoing foce. 21 Damped oscillations When fictional and esistive foce educe the amplitude (enegy) of the oscillation 22 Resonance When diving feq. of the osc. is equal to natual fequency gives max amplitude atto a Impotant Equations fo A2 Physics Pepaed by Faisal Jaffe - 1

2 Unit 2: Themal Physics (Topic 11, 12, 13) 1 Mole: amount of substance, n eg 1 mole cabon=12g, 1 mole of oxygen=16g, 1 mole of wate=18g 2 Avogado constant, N A Constant numbe of molecules o atoms in 1 mole= paticles 3 Bownian motion Random, jeky, haphazad, zigzag motion of molecules in liquid o gas 4 Absolute Tempeatue, K Tempeatue in kelvin scale T/K=θ/ o C Ideal gas equation pv=nrt P=pessue, V=volume, T=temp in Kelvin, n numbe of moles, R=univesal gas constant pe mole=8.3jmole -1 K Ideal Gas - gas that obeys ideal gas equation at all pessues, volumes, tempeatues, - molecules do not exet foces on each othe when collide, - the collision between the molecules is pefectly elastic 7 Kinetic theoy of ideal gas - Matte is made of tiny paticles called atoms o molecules, - These paticles ae in constant, andom motion, - Paticles collide with each othe and collision is pefectly elastic, - Paticles apply no foce on each othe when collide, - Motion of paticles is geate in gas, less in liquid and least in solids, - Volume of paticles in gas is negligible compae to the volume of gas. 8 Kinetic theoy of ideal gas pv = Nm c o p = ρ c N is the total numbe of molecules, m is the mass of a molecule, p the pessue, V the volume of containe, c the aveage of squae of the velocities of molecules, = ρ, the density of gas. 9 Othe gas equations pv = NkT R=univesal gas constant (pe mole) =8.3Jmole -1 K -1 R = n k k=boltzmann constant (pe molecule)= JK -1 R = N k, Avogado no molecules/mole N 10 Aveage of E molecules E = kt T, the tempeatue in kelvin, k, the boltzmann constant 11 Heat and tempeatue Heat is a fom of enegy measued in joules Tempeatue is the degee of hotness of an object measue in o C o K 12 Intenal enegy ΔU In ideal gas, it is the sum of kinetic enegies of all molecules In eal gas, it is the sum of kinetic and potential enegies of all molecules 13 Law of themodynamics The incease in intenal enegy (ΔU) of a system is equal to the sum of heat enegy added to the system and the wok done on it. U = Q + W Q is the heat enegy and W(=pΔV), is the wok done on the system 14 Themal equilibium When all sections of a system ae at same tempeatue 15 Physical popeties of matte when heated - most mateials expand upon heating, eg mecuy in glass themomete - esistance of metals inceases when the tempeatue inceases, eg 16 Themocouple themomete (junction between coppe and ion wie) 17 Specific heat capacity:..amount of heat equied to aised the tempeatue of unit mass of a substance to one degee 18 Themal capacity, C unit J/ o C 19 Specific latent heat:..amount of heat equie to change the state of unit mass of matte without incease of tempeatue themocouple themomete a) wide ange (-200 o C to 1500 o C) b) can stoe data electonically c) small size easy to manage d) ecod vey apid change of tempeatue e ) can measue the tempeatue of small objects C = c = Q c, the specific heat capacity, Jkg -1o C -1 m θ m, the mass of an object, kg Δθ, the change in tempeatue, o C P t ΔQ, amount of heat enegy, J c = m θ P, the powe of electical heate, W t, ON time fo electical heate, s o C = c m..heat equied to incease the tempeatue of a whole body..of fusion fom solid to liquid..of vapoization fom liquid to gas l = Q P t = l m m = Q P t = m m unit J/kg unit J/kg Always I > I fo the same substance Impotant Equations fo A2 Physics Pepaed by Faisal Jaffe - 2

3 Unit 3: Foce fields (topic fom syllabus 8, 17, 18, 21, 22) Gavitational field 1 Newton s law of gavitation Evey two objects attact each othe with foce diectly popotional to thei masses and invesely popotional to the squae of the distance between them 2 Gavitational foce F between two masses = G m m F the foce in newton, m 1 & m 2 masses, G univesal foce constant Nm 2 kg -2 3 Eath s Gavitational mg = F = G M m M e the mass of eath, R the adius of eath foce on mass m R 4 Gavitational field stength, g g = G M Foce pe unit mass placed at a point in a R gavitational field=9.81nkg -1 5 Gavitational potential enegy, E p E = G M m = mg 6 Gavitational potential φ = E m = G M 7 Geostationay obit T 4π = GM Electic field 8 Coulomb s law of electostatic F = 1 Q Q 4πε = C -2 Nm 2 9 Electic field intensity, E, due to chage Q 10 Electic field intensity, E, between the two chaged plates 11 Electic potential, V Capacitance 12 Capacitance, C 1 4πε E = F q = 1 4πε Q V = E = V d Q 4πε wok done against the gavity on binging the mass to distance above the suface of the eath (=R+Δh) Potential enegy pe unit mass The squae of the peiod is popotional to the cube of the adius of obit q 1, q 2 chaged objects in coulombs, the distance between the chaged objects, ϵ o the pemittivity of fee space= C 2 N -1 m -2 - foce on a unit chage q at any point aound anothe chage Q - out fom positive end to negative chage V the potential diffeence between the plates d the distance between the plates E is unifom between the plates, unit is Vm -1.. wok done in binging the point chage fom infinity to a point in an electic field C = Q atio of chage (Q) stoed to potential diff.(v) V between conducto, unit Faad, mf and µf 13 Electic pot. enegy stoed in a capacito E = QV = CV = Q - Capacito is use to stoe chages o enegy, C - has two plates and insulato in between 14 Factos affecting A A the aea of paallel plates, d the distance capacitance C = ε ε d between them, ϵ o pemittivity of fee space, ϵ elative pemittivity of dielectic 15 Relative pemittivity ϵ Capacitance with dielectic divided by capacitance with vacuum, no units 16 Capacitos connected.. paallel C = C + C.. seies in... + Magnetic fields 17 Magnetic field Foce of field aound magnets o cuent caying conducto 18 Magnetic flux density B the magnetic field stength o foce pe unit length of conducto, unit tesla (T) 19 Magnetic flux Poduct of magnetic flux density (B) and aea (A) nomal to the magnetic field lines, unit webe (Wb) o tesla mete squae (T m 2 ) φ = BAsinθ 20 Foce (F) in magnetic field..on cuent caying conducto F = BILsinθ..on moving chage q with speed v F = Bqvsinθ 21 Specific chage of e electon e/m m = v The atio of chage to mass of an electon B 22 Faaday`s law of EM Emf poduce is diectly popotional to ate of change of magnetic flux linkage induction 23 Hall pobe Use to find amount of magnetic field by ceating hall voltage V H in a conducto Impotant Equations fo A2 Physics Pepaed by Faisal Jaffe - 3

4 Unit 5 Moden Physics (Topics fom syllabus 25, 26 and 27) Chages Paticles 1 Photoelectic effect Emission of electons fom metals when e.m. adiations fall on it. Poof of light as paticles that is paticle stikes paticle emits 2 Photoelectic effect: Popeties a) instantaneous b) only happen if the feq is above minimum level c) each metal have its own feq d) ate of electons emits is popotional to intensity 3 Theshold feq f o The minimum feq of wave equied to emit the electons fom the metals, each metal have its own theshold fequency. 4 Max Plank Equation E = fh E the enegy, f the feq and h the Planks constant= Js 5 Photon Light as packets and enegy of these packets ae quantized, only on cetain fixed levels. 6 Wok function enegy The minimum amount of enegy equie fo electon to escape, φ = hf wok function enegy in J, f o the theshold feq, h planks constant 7 Photoelectic equation E = hf = φ + m v E = hf = hf + m v 8 de Boglie wavelength, λ Equation of wave paticle duality λ = h p is momentum of the paticle p 9 Electomagnetic specta Continuous specta: spectum of Line specta: spectum of only few 10 Quantization of enegy levels in atomic obits all colous and wavelengths E = E E = hf colous and wavelengths shown as lines When electon jump fom: lowe to highe enegy state absob enegy highe to lowe enegy state emit enegy Nuclea Physics 11 Atomic mass unit,1u 1u= kg Equal to one-twelfth of the mass of cabon-12 atom 12 Mass deficit Diffeence between the total mass of sepaate nucleons and combine nucleus 13 Mass Enegy Equation E = mc E is the enegy, m the mass and c the speed of light 1u = 931MeV 14 ev the unit of enegy 1eV= J 1MeV= J 15 Binding enegy Enegy equivalence of mass deficit, enegy equie to sepaate the nucleons 16 Binding enegy pe nucleon Total enegy equie to sepaate the nucleons divided by the numbe of nucleons (study the gaph on page no 369 of AS Physics by Chis Mee...) 17 Nuclea fusion Smalle nuclei combine togethe to fom lage nuclei, equie high tempeatue and pessue 18 Nuclea fission Heavy nuclei bombaded with neutons, split into smalle nuclei, elease enegy Quantum Physics 19 Photoelectic effect Emission of electons fom metals when e.m. adiations fall on it. Poof of light as paticles 20 Photoelectic effect: Popeties a) instantaneous b) only happen if the feq is above minimum level c) each metal have its own feq d) ate of electons emits is popotional to intensity 21 Theshold feq f o The minimum feq of wave equied to emit the electons fom the metals, each metal have its own theshold fequency. 22 Max Plank Equation E = fh E the enegy, f the feq and h the Planks constant= Js 23 Photon Light as packets and enegy of these packets ae quantized. 24 Wok function enegy The minimum amount of enegy equie fo electon to escape, φ = hf 25 Photoelectic equation E = hf = φ + m v E = hf = hf + m v wok function enegy in J, f o the theshold feq, h planks constant Impotant Equations fo A2 Physics Pepaed by Faisal Jaffe - 4

5 26 de Boglie wavelength,λ Equation of wave/ paticle duality λ = h p 27 Electomagnetic specta Continuous specta: spectum of all colous and 28 Quantization of enegy levels in atomic obits wavelengths E = E E = hf p is momentum of the paticle Line specta: spectum of only few colous and wavelengths shown as lines When electon jump fom: lowe to highe enegy state absob enegy highe to lowe enegy state emit enegy Impotant Equations fo A2 Physics Pepaed by Faisal Jaffe - 5

Important Equations in Physics (A2) s is the arc length in meters r is the radius of a circle in meters 6 Angular speed, ω in radians/seconds

1 Important Equations in Physics (A2) Unit 1: Non-uniform Acceleration (Topic 7 and 14) 1 Base units Length meters Mass kilograms Time seconds 2 Multiples of units Tera T 10 12 Giga G 10 9 Mega M 10 6