CIRCULAR MEASURE Linear Displacement Displacement in a straight line Linear velocity Rate of change of angular displacement Angular Displacement Anglesubtended at the centre when an position A to position B on a circular track Angular velocity Rate of change of angular displacement W O t For A complete revolution v rW s object movesfrom linear velocity It T W radius We 298 angular velocity x CentripetalForce Force requiredfor an XY Z havethesame object to move in a circle Is directedtowards hey t If In one centre or the circle 2 Fe Fc MrW Vx Ny Ve as Fe my verw considering Mv w theradiusratio Centripetal acceleration F ma mas mu w ma mu r mas mrw Conical Pendulum as rw r a a NW Radian Anglesuspended at the centre of a F Fc sine circle by an arc equal to its radius vertical Circular motion T W COSA Tmax MY't 008180 p Feng kg Tano Mmg vg Tan Tan HorizontalCircular Motion I Iw Fc T 1 Mv2 r Imax tm900270 Tma 0270 I gooo p go Imax Mf Imax p Imax Yu mg mg 90 0900TmaxMftmgeos w Tmax vitoFe T woos mglosco my mg Niv r Tmax ME1mgCos GRAVITATION law ofGravitation Force of attractionbtw two pointmasses is directly proportional to the product of the masses and inversely Fa GMima proportional to the square of the distance btw their centres R2 moon Earth Relationship b w g anda null Point Earth W a moon Newton's magcon Mlg Amfm g GM R2 pint objectof gig mass m id Atthe null point t MELHEM Gravitational FieldStrength g Fr distance'm in ofspace where amassexperiences aforce GravitationalField Region ofattraction experiencedby a unitman placedwithinthefield Force Satelliteorbitting a planet Geostationary Orbit equatorial orbit aboveequator satellite satellitemoves fromwesttoeast samedirectionas Earth period is 24 hours same period as spinningon Earth FcFa m ay ma M G GMT 0 at infinity is zero Wi 913 mus KE 0.5 KE 0.5m Ft 0 Gravitational potential GM awayfrominfinity it becomes ve field to move unit mass work is done by the towards the sourcemass o DO Of 08 24 93 DO GE far a n so am r Gravitational PotentialEnergy work done in moving a point mass from infinity to a point within the gravitational field eaknw 0 gg moon Escape velocity KE MI T2 Im GaininGPElossinKE 3ham ME at surface g Gig g lg matmvesi Vest Gm Re o 129ft 2 Vesc Vest µ GREGME GERE X Ferpositionosboth oedaugto Omdgento E DO m E ft H Eam n gift If grill ppl.mg Engh mi Binary Star System M Ri yo MZ Ra g Fa Fa Fa Fc Jim anime MIRw2 Rita Ri RI SIMPLE TE GMEM ar y Miike rehang TE KE APE GMem TEGMENz GPE GME.me y ie dem E GPEDO.me EK GMem satellite a Derevation of GPEmgh Satelliteorbitting a planet MIRIN 2 MzRzw2 MERWE MI Rz Mz RI Harmonic MOTION acceleration Relation an x x SAMis oscillatory motion Accelerationanddisplacement proportional Accelerationanddisplacement inopposite directions N two W xo2 x2 Ellipse Em Choo energy Cho xowasinw s.pro D to now now now now 7 a wax linked a walxosinwt Velocity at SHM w IW nor x2 no maximum displacement a displacementfrommean position PotentialEnergy kinetic Energy TotalEnergy KE 12MV2 K E 12M W yo W Xo x2 KEIM now potential C xosinwtddf xoweoswtdvdte 2 TE MaxKE x O atMaxKE TE Imway y KE PE TE KE PE pE ymw2y2 GraphsforKEPEandTEagainsttime mE1J 2 Energy knw'tTotal KE 42MW 103 ME 42mn40 ll Sinwt KE12Mw2lxo3xo3in2wtpq.q.yzmwryo2 kinetic 42MW'd ogzwtP.E 12mW'xisintut PE energy Ho Potential Energy FreeOscillations intheabsence of a resistivemedium DampedOscillations Oscillations occurring inthepresence of a resistivemedium Oscillations occurring LightDamping air moderateDamping water Heavy Damping Honey resonance Every mechanicalsystem hasits natural Kemeny of oosillation fundamentalfrequency If frequencyof aforcedoscillator Pa Boyle's Law v If y.fi yY1fgg fundamentalfrequency which results in a maximumtransferof energyandtheamplitudeofthe mechanicalsystemreachesmaxvalue 2MAI n SICS Vat Charles law Pat Gay Lussac's law IdealGas Formula PV n RT n Moles of gas R UniversalGas Constant 8.31 pay Pay P Pressure V volumeofGas T Temperature Kelvin Ideal Gas Assumptions a molecules move in constantandrandom motion 2 collisions betweenmolecules and container walls are completely elastic 3 Pressure is due to collisions between molecules andcontainerwalls 4 IdealGas molecules are free of anyintermolecularforcesof attraction 5 volumeof molecules is negligible in comparasionto the containervolume Pressureof IdealGas D 43 Pecs Derevation Rn ex m D UniversalGasConstant n z t mass e C velocity For molecule m Bp p m Bex m Rex DP 2am 9m E sp s Time t 2L Cx E 2AM IL CX F Cy M D Cx'm L A mi nm piece m v ECZ ECR Cy's t ECE ECz2 Lex'ssecy 3 0 23 ee ed 3 D I ex2 Pee Total KineticEnergy Average kineticEnergy Pv Nkt M ee 32NRT 12MECD 32NRT 12Mees IMU 12 32NRT N KMC 32ART N Yzma 3 2 PV N Zz KT P 13 Pee 32MNRT 42MCC 312RNAT 42m62 D 43 Mv cc PV NKT Mee 32PV 42M C2 KE 32PV 3PV 312NRT NA Avogadro's constant 32 KT Yam e CZ AVG KE 32kt Cprogimenanppeed andTemperature 43040 MnRT cr.m.sn T go 311 k Boltzmann Constant d MCAT Energy required toraise the temperatureof 1kg of a substance by 10C I k SpecificlatentHeat Q ML Energy requiredfor a 1kg substance to undergo a change in state Elimination oferror internal Energy of Gases Elimination oferror latent Heatoffusion latentHeatofVaporisation TotalEnergy KE t PE t t O k ml IdealGases Total Energy KE offo 0880 Pat ke mil Workdonebygas Px IN Specific HeatCapacity f 1114 11h41 SetupA SetupB Mi Ma l L O mi me ÉYÉiÉ p Pat Malek Pit Mil Pat MIL L thPEP WB DWCon compression First law of Thermodynamics DO DU t DW By Du InternalEnergy Da Energysupplied to gas LECTROSTATICS Columb's law Forceof attraction between two point charges is directlyF gotQpg proportional to theproductof the charges andinversely proportional permitivityof freespace the square of the distancebetween their centres Electric Field Strength Force per unit positive charge E x to j q Graphs of Electric Field Strength Electric Potential Workdone to move a unit positivechargefrominfinity to a against distance Ent point within the electric field X M É GraphOf Evs R for a conductor E Establishing link l Ne Op O y qp E dr day q q IL Graphs of ElectricPotential againstdistance WE 90N in EPE Loss in KE DNg Fieldstrength MT'd QS a of w avg arvo's U 12mV's ta um a ng rim q rim I ta g closest approach e r field done by the Foran accelerating electron Gradient of we chargemeans work r GraphofVvs R L sign is considered rim Distance A Q ppgp graph E Electric Electric PotentialEnergy 4780 du a x B OB Coggin KE gainin EPE 2112mn q yo Q x m 4 09 0 ULEMA CAPACITANCE Capacitance Ratio of the amountof charge stored on potentialenergy a Electric DELETE II Potential Potential raw new f Q Cv seriescapacitor I ElectricPotentialEnergy V3 e 02oz 03C t Allcapacitors havesamecharge capacitance a vintage the plate with go Otc c I t t z d I MaxSafeWorking Voltage Parallelcapacitors Allcapacitorshavesamevoltage capacitor is ratedyou5,301 capacitance a voltage ElectricPotentialEnergy a capacitance 15 11 12 13 It Discharging of a 03 2 you v go S 4301 OC too Or C MTLEOR capacitor o y GUTCIVtC2V2tC3V3 CT Clt 2 03 Miko Constant T.me IRC R Resistance ccapacitance Timetakenfor a I loethe v Voetre 0 0 ethe capacitor to discharge MAGNETISM of space where a moving charge experiences a force Fm Bgr B Magnetic Flux Density q charge v velocity TY CrossFieldmagneticandElectricFields are perpendicular Fleming'sCAR MagneticField Region Fe Fm M at Bar Ism BqV Eq mu r if if if FB Fm FE v eEB Fm e Fe V FB Fm Fe N Bar Fm Fe HALLPROBE Bgr Eq BU E v d v N Blige Y I nae Blade Vit B V Intel d Vit HallVoltage v start End Fm BIL Tesla B F1 Tesla is the unit of magneticfluxdensity I Tesla of magneticfluxdensity occurs when a straight wire carrying a current 081A perpendicular to the magnetic field exerts a force of IN per metre unitlength Force of attraction between 2 wives Torque Fm W Fm B L BIL W Fm 2 107 BIA 2 L B 2 10 7 I d Magneticfluxdensity at a point perpendicular fromthewire I q 7 Fm 2 10 Ii IzL d LECTRO MAGNETIC for BA I IDUCTION of turns NBA Faraday'sLaw Rate of change of magneticflux is the induced EMF voltage J E Of 018 t or E doldt in the circuit E DO t Lena's law Lena's law can be used to determinethe an n number directionofinducedcurrent in a solenoid Inducedcurrent always flows in the direction apposingthechangecausing it Asthe magnet enters exits thecoil mechanical energy is usedup Damping Overcoming Damping Use a resistor as it leads to lessercurrent in overcoming attractive repulsiveforces sima tis thereforelesser opposition For a wire cutting a magnetic field E BLU Eddy currents Asthediscspins rateofcutting magneticfluxlines is notthesame foreverypartofthediscThismeans differencesin EMF inducedThis causeseddycurrentsTheseeddy currents dissipateenergy therefore they cause a amplitude energy Lena's t Faraday'sLaw Ea B a o En n do It I N g LTERNATING CURRENTS diode Normal AC Currentwave v HS loss in negative gradientof O us t Half wave Rectification Full wave Rectification Advantage HalfWave 11 Lessercomplexity n Fullwave lesser power loss Na on I Disadvantage Halfwave Greater powerloss vout FullWave e A process bywhichthe outputvoltage More complex does not fall to zero Parallel capacitor combination Smoothing on capacitor current voltage in Al 1 losinwt N Vosinwt Iims Vms Ig Prins Po 2 y t it t meansgreatersmoothing Series capacitor combination means lesser smoothing Forsquare waves Transformers a No puppy Veg StephSquare steps mean Step3 Root 3 To Is v02 Vo hereUrms No Tp M Is PPrimaryboil f Secondary witmberog turns VAN UM PHYSICS ElectronVolt Theamount of kineticenergy an electron gains as it accelerates 19 througha potentialdifference of 1 volt eV Workdonein joules 1.610 Photon A photon is a quantum of electromagnetic radiation having a h Planck's constant fixed amount of energy Ehf Workfunctionenergy Energyrequired E 0 KE work function to bring electrons to thesurface ofthemetal energy Thresholdfrequency Minimum frequency hf info KE fo thresholdfrequency for photoelectric effect Dual Nature Of EMR EMR can proving it exists as waves need a threshold frequency to happen proves undergo diffraction Photoelectriceffect it exists as particles as in case of waves photoelectric effect would haveoccurred at any frequency Intensity Power Enga area 14nptphotoelectriccurrent l np hf 89Iconstant npM y photoelectric current u Electrons have a dual nature like EMR De Broglies Equation wavelength of moving particles n momentum v hp p Photon Pressure n 600 nm P 2mW v0 I n Mmr V2 240mhm y I axiom h Mp gyp 1 Photon3.31510195 2 Nophotons in Asecond6.0 1015 Power Np Energy 1 Energyof time 3 Momentumof 1 photon 1.1111027ns Nse DeBroglie's equation Spectral lines n Absorpion Ey Ez q mtg V9 42mV Nq KELE A M DE Bar D Bgr mu h a e em MY BqV f Bgr at TY M Total Momentum 6.63 1012ns TotalMomentum np momentumof photon 5 Force F DD 6.63 10 N t 6 Pressure P Force 5.53 10 6 Pa Area d How do spectral lines provideproof of discrete energy levels spectral lines correspond to discrete wavelengths Discrete wavelengths mean photons have a fixed amount of energy Emission h photons areemitteddue to energy change of electrons Fixed energychange means discreteenergy levels Identifying gases through spectral lines Gases have electrons in energy levels certain wavelengths correspond to certain photons whichelectrons gain energy to gofrom a lower to higher energylevel Electrons thendeexcite and emit photons in all directions displayedon the spectrum by darklines These wavelengths are NUCLEAR PHYSICS Binding Energy Energy required Infinity E Dme to split all nucleons in a nucleus to Fe 56 Binding Energy m mass defect Bindingenergy pernucleon BindingEnergy ev Total nucleons Them Fission Heavy nuclei split into lighter nuclei Fusion lighternuclei fuse to form heavy nuclei Fusion Fission MEnber Energy Released Absorbed EBindingEnergy Products EBindingEnergy Reactants RADIOACTIVITY t t's half life Timetaken for the at m moe activity of a radioactive sample to Decayconstant n nt's half its initial value Probabilityofdecay of a m Noe nt nucleusper unit time c coe Ao Aoe ath Activity Bg AN A Aoe A Activity of the sample of sample N Number of radioactive particles C Count rate m Mass YE e nt In la ntyz Ln2 nth 2 th Ln MEDICAL PHYSICS X Rays o Production at look Efent to beemitted y from the cathode accelerating to theanode is age metal filamentc athode Anodecollision results in X Ray photon emission Ill Aluminium sheet blocks soft X Rays no use for medicalpurposes Attentuation Loss in intensity of x due to exposure of living matter rays Ln u I Joe u u linear attentuation constant Xyz 42 thickness that causes intensity to halve Contrast X Rays Varying levels of blackness of differentobjectsin an image How to increase useartificial contrast increase exposure time Thermionic emission causes electrons Use slouroscent backing material Sharpness X Rays How well edges of different objects in an image can be distinguished How to increase Decrease size of anode plate Reduce aperture size CTScans ComputedTomography Uses x Rays Object split into Advantages slices Imageof eachslice taken from multipleangles Thousands ofimagesofeach slice processed to create a 2 Dimage Done for all other slices All slices 2Dimages processed to make3D image 3 D image can be rotatedand observed can be done relatively quickly in comparasion to Provides MRI good contrast can aid in treatment of brain tumors Disadvantages Quite expensive Exposure to large radiation dose PET Scan Positron Emission tomography uses a radioactive tracer thats injected in the patient What is atracer Substanceinjectedinto apatient absorbed by tissues Howdoes thishelp Prevention of surgery therefore no risk of infection Tracer Flourine 18 emits a positron Positron is antimatter it searches for an electron and bothannihilate one another Annihilation releases 2 gamma photons ofequalenergy in opposite directions Donutshapedgamma ray detector is placed around the patient Time delay betweenthe 2 gamma ray photons travelling to the detector aids in finding exact location of annihilation Ultrasound Specific Acoustic impedance12 pc Density of medium How is it produced speedof ultrasound in themedium Ultrasound detectors contain Intensity Reflection Coefficient yr piezoelectriccrystals Li 22 Lithe u Piezoelectriccrystals contain Attentuation of ultrasound positiveand negativesilver A scan ultrasound coated electrodes ultrasound transmitters emitultrasound on the skinofthe I toe Currentappliedcausescrystals patient Asthe ultrasound travels boundaries reflect a fraction AC current causes crystals of the ultrasound whilethe rest penetrates Thereflected wave is detected by thetransmitter to vibrate where the detected current is amplifiedandpulses They vibrate at resonating to change shape frequencyproducing ultrasounds Advantage No seriousthreat as they are displayed on a CRO theecho time can be used to of the boundary do not containionizing B Scan Ultrasound radiations A Bscan is a Disadvantage combination of calculate the thickness A scanwhich istakenfrom a varietyofdifferentanglesTheindividualpulses obtainedaregathered Forairfilled cavities e lungsanalysedandprocessed by a computer whichsuperimposes these g ultrasound is notused because multiple echoes on top of eachother thereby gathering a imagelacks sufficientdetails twodimensionalimage ND STRONOMY COSMOLOGY L It is theabsolutemeasureof thetotalpower of theelectromagnetic radiation emittedby a star RadiantFluxIntensity F Luminosity passing normally through a surface perunit area Year Distancetravelled bylight in a F L light Fa vaccum in a time of one stud year StandardCandles It is a class of stellarobject whichhas a known luminosityand whose distance can be determinedby calculation using itsradiantfluxintensity Luminosity I II andluminosity I Wien'sdisplacement law The linkbtw observedwavelengthoflight and temperature amax a T amax b T hated beWiens Displacement Constant 2.898x 10 3mktYak Stefan Boltzmann law The luminosity of a star does not thesurfacetemperature of the star It 4 MT8 T re also depends on the physical state of the star Stefan boltzmann law for luminosity 8 5.67 10 8 WM 2k 4 Doppler RedShift Theincrease in observed wavelength of electromagnetic waves dependjust on due tothe recession from thesource Doppler BlueShift The decrease in observed wavelength of electromagnetic waves due tothe advancement of thesource towards theobserver off DI We werelativevelocity ofstarfrom Earth a speed of light no Wavelength in Lab Hubble's law Therecessionalvelocity of a galaxy from Earth is proportionalto thedistanceof the galaxy from Earth Ho Hubble's constant workedout ur recessional speed of galaxy Nra d ur Mod d distanceof galaxy from Earth Throughhubble's It law it f observed frequencyfrom star correctly proves that therefore provides evidenceof Ageof theuniverse 1 Ho the universe is constantly expanding the BigBang ZEESHAN ALAM KHAN TEACHER SIR AFTAB SAAD
