Note that formulas are not given on the test Each formula row contains a description of the variables or const ants that make up the formula along with a brief explanation of the formula Kinematics ave ave average velocity displacement elapsed ti ID: 12347
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SATSubjectPhysicsFormulaReferenceThisguideisacompilationofabout ftyofthemostimportantphysicsformulastoknowfortheSATSubjecttestinphysics.(Notethatformulasarenotgivenonthetest.)Eachformularowcontainsadescriptionofthevariablesorconstantsthatmakeuptheformula,alongwithabriefexplanationoftheformula.Kinematics vave=x t vave=averagevelocityx=displacementt=elapsedtime Thede nitionofaverageve-locity. vave=(vi+vf) 2 vave=averagevelocityvi=initialvelocityvf= nalvelocity Anotherde nitionoftheav-eragevelocity,whichworkswhenaisconstant. a=v t a=accelerationv=changeinvelocityt=elapsedtime Thede nitionofacceleration. x=vit+1 2a(t)2 x=displacementvi=initialvelocityt=elapsedtimea=acceleration Usethisformulawhenyoudon'thavevf. x=vft 1 2a(t)2 x=displacementvf= nalvelocityt=elapsedtimea=acceleration Usethisformulawhenyoudon'thavevi. erikthered.com/tutorpg.1 SATSubjectPhysicsFormulaReferenceKinematics(continued) v2f=v2i+2ax vf= nalvelocityvi=initialvelocitya=accelerationx=displacement Usethisformulawhenyoudon'thavet. Dynamics F=ma F=forcem=massa=acceleration Newton'sSecondLaw.Here,Fisthenetforceonthemassm. W=mg W=weightm=massg=accelerationduetogravity Theweightofanobjectwithmassm.ThisisreallyjustNewton'sSecondLawagain. f=N f=frictionforce=coecientoffrictionN=normalforce The\PhysicsisFun"equa-tion.Here,canbeeitherthekineticcoecientoffric-tionkorthestaticcoecientoffrictions. p=mv p=momentumm=massv=velocity Thede nitionofmomentum.Itisconserved(constant)iftherearenoexternalforcesonasystem. erikthered.com/tutorpg.2 SATSubjectPhysicsFormulaReferenceDynamics(continued) p=Ft p=changeinmomentumF=appliedforcet=elapsedtime Ftiscalledtheimpulse. Work,Energy,andPower W=FdcosorW=Fkd W=workF=forced=distance=anglebetweenFandthedirectionofmotionFk=parallelforce Workisdonewhenaforceisappliedtoanobjectasitmovesadistanced.FkisthecomponentofFinthedirec-tionthattheobjectismoved. KE=1 2mv2 KE=kineticenergym=massv=velocity Thede nitionofkineticen-ergyforamassmwithveloc-ityv. PE=mgh PE=potentialenergym=massg=accelerationduetogravityh=height Thepotentialenergyforamassmataheighthabovesomereferencelevel. erikthered.com/tutorpg.3 SATSubjectPhysicsFormulaReferenceWork,Energy,Power(continued) W=(KE) W=workdoneKE=kineticenergy The\work-energy"theorem:theworkdonebythenetforceonanobjectequalsthechangeinkineticenergyoftheobject. E=KE+PE E=totalenergyKE=kineticenergyPE=potentialenergy Thede nitionoftotal(\me-chanical")energy.Ifthereisnofriction,itisconserved(staysconstant). P=W t P=powerW=workt=elapsedtime Poweristheamountofworkdoneperunittime(i.e.,poweristherateatwhichworkisdone). CircularMotion ac=v2 r ac=centripetalaccelerationv=velocityr=radius The\centripetal"accelerationforanobjectmovingaroundinacircleofradiusratveloc-ityv. Fc=mv2 r Fc=centripetalforcem=massv=velocityr=radius The\centripetal"forcethatisneededtokeepanobjectofmassmmovingaroundinacircleofradiusratvelocityv. erikthered.com/tutorpg.4 SATSubjectPhysicsFormulaReferenceCircularMotion(continued) v=2r T v=velocityr=radiusT=period Thisformulagivestheveloc-ityvofanobjectmovingoncearoundacircleofradiusrintimeT(theperiod). f=1 T f=frequencyT=period Thefrequencyisthenumberoftimespersecondthatanobjectmovesaroundacircle. TorquesandAngularMomentum =rFsinor =rF? =torquer=distance(radius)F=force=anglebetweenFandtheleverarmF?=perpendicularforce Torqueisaforceappliedatadistancerfromtheaxisofro-tation.F?=FsinisthecomponentofFperpendicu-lartotheleverarm. L=mvr L=angularmomentumm=massv=velocityr=radius Angularmomentumiscon-served(i.e.,itstaysconstant)aslongastherearenoexter-naltorques. erikthered.com/tutorpg.5 SATSubjectPhysicsFormulaReferenceSprings Fs=kx Fs=springforcek=springconstantx=springstretchorcompression \Hooke'sLaw".Theforceisoppositetothestretchorcom-pressiondirection. PEs=1 2kx2 PEs=potentialenergyk=springconstantx=amountofspringstretchorcompression Thepotentialenergystoredinaspringwhenitisei-therstretchedorcompressed.Here,x=0correspondstothe\naturallength"ofthespring. SimpleHarmonicMotion Ts=2r m k Ts=periodofmotionk=springconstantm=attachedmass Theperiodofthesimplehar-monicmotionofamassmat-tachedtoanidealspringwithspringconstantk. Tp=2s l g Tp=periodofmotionl=pendulumlengthg=accelerationduetogravity Theperiodofthesimplehar-monicmotionofamassmonanidealpendulumoflengthl. erikthered.com/tutorpg.6 SATSubjectPhysicsFormulaReferenceGravity Fg=Gm1m2 r2 Fg=forceofgravityG=aconstantm1;m2=massesr=distanceofseparation Newton'sLawofGravitation:thisformulagivestheattrac-tiveforcebetweentwomassesadistancerapart. ElectricFieldsandForces F=kq1q2 r2 F=electricforcek=aconstantq1;q2=chargesr=distanceofseparation \Coulomb'sLaw".Thisfor-mulagivestheforceofattrac-tionorrepulsionbetweentwochargesadistancerapart. F=qE F=electricforceE=electric eldq=charge Achargeq,whenplacedinanelectric eldE,willfeelaforceonit,givenbythisformula(qissometimescalleda\test"charge,sinceitteststheelec-tric eldstrength). E=kq r2 E=electric eldk=aconstantq=charger=distanceofseparation Thisformulagivestheelec-tric eldduetoachargeqatadistancerfromthecharge.Unlikethe\test"charge,thechargeqhereisactuallygen-eratingtheelectric eld. erikthered.com/tutorpg.7 SATSubjectPhysicsFormulaReferenceElectricFieldsandForces(continued) UE=kq1q2 r UE=electricPEk=aconstantq1;q2=chargesr=distanceofseparation Thisformulagivestheelec-tricpotentialenergyfortwochargesadistancerapart.Formorethanonepairofcharges,usethisformulaforeachpair,thenaddalltheUE's. V= WE q=UE q V=potentialdi erenceWE=workdonebyE eldUE=electricPEq=charge Thepotentialdi erenceVbetweentwopointsisde nedasthenegativeoftheworkdonebytheelectric eldperunitchargeaschargeqmovesfromonepointtotheother.Alternately,itisthechangeinelectricpotentialenergyperunitcharge. V=kq r V=electricpotentialk=aconstantq=charger=distanceofseparation Thisformulagivestheelectricpotentialduetoachargeqatadistancerfromthecharge.Formorethanonecharge,usethisformulaforeachcharge,thenaddalltheV's. E=V d E=electric eldV=voltaged=distance BetweentwolargeplatesofmetalseparatedbyadistancedwhichareconnectedtoabatteryofvoltageV,auni-formelectric eldbetweentheplatesissetup,asgivenbythisformula. Circuits V=IR V=voltageI=currentR=resistance \Ohm'sLaw".ThislawgivestherelationshipbetweenthebatteryvoltageV,thecurrentI,andtheresistanceRinacircuit. erikthered.com/tutorpg.8 SATSubjectPhysicsFormulaReferenceCircuits(continued) P=IVorP=V2=RorP=I2R P=powerI=currentV=voltageR=resistance AllofthesepowerformulasareequivalentandgivethepowerusedinacircuitresistorR.Usetheformulathathasthequantitiesthatyouknow. Rs=R1+R2+::: Rs=total(series)resistanceR1= rstresistorR2=secondresistor::: Whenresistorsareplacedendtoend,whichiscalled\inse-ries",thee ectivetotalresis-tanceisjustthesumofthein-dividualresistances. 1 Rp=1 R1+1 R2+::: Rp=total(parallel)resistanceR1= rstresistorR2=secondresistor::: Whenresistorsareplacedsidebyside(or\inparallel"),thee ectivetotalresistanceistheinverseofthesumofthere-ciprocalsoftheindividualre-sistances(whew!). q=CV q=chargeC=capacitanceV=voltage Thisformulais\Ohm'sLaw"forcapacitors.Here,Cisanumberspeci ctothecapac-itor(likeRforresistors),qisthechargeononesideofthecapacitor,andVisthevolt-ageacrossthecapacitor. erikthered.com/tutorpg.9 SATSubjectPhysicsFormulaReferenceMagneticFieldsandForces F=ILBsin F=forceonawireI=currentinthewireL=lengthofwireB=externalmagnetic eld=anglebetweenthecurrentdirectionandthemagnetic eld ThisformulagivestheforceonawirecarryingcurrentIwhileimmersedinamagnetic eldB.Here,istheanglebetweenthedirectionofthecurrentandthedirectionofthemagnetic eld(isusu-ally90,sothattheforceisF=ILB). F=qvBsin F=forceonachargeq=chargev=velocityofthechargeB=externalmagnetic eld=anglebetweenthedirectionofmotionandthemagnetic eld Theforceonachargeqasittravelswithvelocityvthroughamagnetic eldBisgivenbythisformula.Here,istheanglebetweenthedirectionofthecharge'svelocityandthedirectionofthemagnetic eld(isusually90,sothattheforceisF=qvB). WavesandOptics v=f v=wavevelocity=wavelengthf=frequency Thisformularelatesthewave-lengthandthefrequencyofawavetoitsspeed.Thefor-mulaworksforbothsoundandlightwaves. v=c n v=velocityoflightc=vacuumlightspeedn=indexofrefraction Whenlighttravelsthroughamedium(say,glass),itslowsdown.Thisformulagivesthespeedoflightinamediumthathasanindexofrefractionn.Here,c=3:8m/s. erikthered.com/tutorpg.10 SATSubjectPhysicsFormulaReferenceWavesandOptics(continued) n1sin1=n2sin2 n1=incidentindex1=incidentanglen2=refractedindex2=refractedangle \Snell'sLaw".Whenlightmovesfromonemedium(say,air)toanother(say,glass)withadi erentindexofre-fractionn,itchangesdirec-tion(refracts).Theanglesaretakenfromthenormal(per-pendicular). 1 do+1 di=1 f do=objectdistancedi=imagedistancef=focallength Thisformulaworksforlensesandmirrors,andrelatesthefocallength,objectdistance,andimagedistance. m= di do m=magni cationdi=imagedistancedo=objectdistance Themagni cationmishowmuchbigger(jmj�1)orsmaller(jmj1)theimageiscomparedtotheobject.Ifm0,theimageisinvertedcomparedtotheobject. HeatandThermodynamics Q=mcT Q=heataddedorremovedm=massofsubstancec=speci cheatT=changeintemperature Thespeci cheatcforasub-stancegivestheheatneededtoraisethetemperatureofamassmofthatsubstancebyTdegrees.IfT0,theformulagivestheheatthathastoberemovedtolowerthetemperature. erikthered.com/tutorpg.11 SATSubjectPhysicsFormulaReferenceHeatandThermodynamics(continued) Q=ml Q=heataddedorremovedm=massofsubstancel=speci cheatoftransformation Whenasubstanceundergoesachangeofphase(forexam-ple,whenicemelts),thetem-peraturedoesn'tchange;how-ever,heathastobeadded(icemelting)orremoved(waterfreezing).Thespeci cheatoftransformationlisdi erentforeachsubstance. U=Q W U=changeininternalenergyQ=heataddedW=workdonebythesystem The\ rstlawofthermody-namics".Thechangeininter-nalenergyofasystemistheheataddedminustheworkdonebythesystem. Eeng=W Qhot100 Eeng=%eciencyoftheheatengineW=workdonebytheengineQhot=heatabsorbedbytheengine Aheatengineessentiallycon-vertsheatintowork.Theenginedoesworkbyabsorb-ingheatfromahotreservoiranddiscardingsomeheattoacoldreservoir.Theformulagivesthequality(\eciency")oftheengine. PressureandGases P=F A P=pressureF=forceA=area Thede nitionofpressure.Pisaforceperunitareaexertedbyagasor\ruidonthewallsofthecontainer. erikthered.com/tutorpg.12 SATSubjectPhysicsFormulaReferencePressureandGases(continued) PV T=constant P=pressureV=volumeT=temperature The\IdealGasLaw".For\ideal"gases(andalsoforreal-lifegasesatlowpressure),thepressureofthegastimesthevolumeofthegasdividedbythetemperatureofthegasisaconstant. ModernPhysicsandRelativity E=hf E=photonenergyh=aconstantf=wavefrequency Theenergyofaphotonisproportionaltoitswavefre-quency;hisanumbercalled\Planck'sconstant". KEmax=hf KEmax=maxkineticenergyh=aconstantf=lightfrequency =workfunctionofthemetal The\photoelectrice ect"for-mula.Iflightoffrequencyfisshinedonametalwith\workfunction" ,andhf� ,thenelectronsareemittedfromthemetal.Theelectronshaveki-neticenergiesnogreaterthanKEmax. =h p =matterwavelengthh=aconstantp=momentum Aparticlecanactlikeawavewithwavelength,asgivenbythisformula,ifithasmomen-tump.Thisiscalled\wave-particle"duality. \r=1 p 1 (v=c)2 \r=therelativisticfactorv=speedofmovingobserverc=speedoflight Therelativisticfactor\ristheamountbywhichmovingclocksslowdownandlengthscontract,asseenbyanob-servercomparedtothoseofanotherobservermovingatspeedv(notethat\r1). erikthered.com/tutorpg.13