Kinematics - erikthered.com

1 SAT Subject Physics Formula ReferenceThis guide is a compilation of about fifty of the most important physics formulas to knowfor the SAT Subject test in physics. (Note that formulas arenotgiven on the test.) Eachformula row contains a description of the variables or constants that make up the formula,along with a brief explanation of the x tvave= average velocity x= displacement t= elapsed timeThe definition of average (vi+vf)2vave= average velocityvi= initial velocityvf= final velocityAnother definition of the av-erage velocity, which workswhenais v ta= acceleration v= change in velocity t= elapsed timeThe definition of acceleration. x=vi t+12a( t)2 x= displacementvi= initial velocity t= elapsed timea= accelerationUse this formula when youdon t havevf. x=vf t 12a( t)2 x= displacementvf= final velocity t= elapsed timea= accelerationUse this formula when youdon t 1 SAT Subject Physics Formula ReferenceKinematics (continued)v2f=v2i+ 2a xvf= final velocityvi= initial velocitya= acceleration x= displacementUse this formula when youdon t have forcem= massa= accelerationNewton s Second Law.

2 Here,Fis thenetforce on the weightm= massg= acceleration dueto gravityThe weight of an object withmassm. This is really justNewton s Second Law Nf= friction force = coefficientof frictionN= normal forceThe Physics is Fun equa-tion. Here, can be eitherthe kinetic coefficient of fric-tion kor the static coefficientof friction momentumm= massv= velocityThe definition of is conserved (constant) ifthere are no external forces ona 2 SAT Subject Physics Formula ReferenceDynamics (continued) p=F t p= changein momentumF= applied force t= elapsed timeF tis called , Energy, and PowerW=F dcos orW=FkdW= workF= forced= distance = angle betweenFand the directionof motionFk= parallel forceWork is done when a forceis applied to an object as itmoves a thecomponent ofFin the direc-tion that the object is =12mv2KE = kinetic energym= massv= velocityThe definition of kinetic en-ergy for a massmwith =mghPE = potential energym= massg= acceleration dueto gravityh= heightThe potential energy for amassmat a heighthabovesome reference 3 SAT Subject Physics Formula ReferenceWork, Energy, Power (continued)W= (KE)W= work doneKE = kinetic energyThe work-energy theorem.

3 The work done by thenetforceon an object equals the changein kinetic energy of the = KE + PEE = total energyKE = kinetic energyPE = potential energyThe definition of total ( me-chanical ) energy. If thereis no friction, it is conserved(stays constant).P=W tP= powerW= work t= elapsed timePower is the amount of workdone per unit time ( , poweris therateat which work isdone).Circular Motionac=v2rac= centripetal accelerationv= velocityr= radiusThe centripetal accelerationfor an object moving aroundin a circle of radiusrat centripetal forcem= massv= velocityr= radiusThe centripetal force that isneeded to keep an object ofmassmmoving around in acircle of radiusrat 4 SAT Subject Physics Formula ReferenceCircular Motion (continued)v=2 rTv= velocityr= radiusT= periodThis formula gives the veloc-ityvof an object moving oncearound a circle of radiusrintimeT(the period).

4 F=1Tf= frequencyT= periodThe frequency is the numberof times per second that anobject moves around a and Angular Momentum =rFsin or =rF = torquer= distance (radius)F= force = angle betweenFand the lever armF = perpendicular forceTorque is a force applied at adistancerfrom the axis of =Fsin is thecomponent ofFperpendicu-lar to the lever angular momentumm= massv= velocityr= radiusAngular momentum is con-served ( , it stays constant)as long as there are no exter-nal 5 SAT Subject Physics Formula ReferenceSpringsFs=kxFs= spring forcek= spring constantx= spring stretch orcompression Hooke s Law . The force isopposite to the stretch or com-pression potential energyk= spring constantx= amount ofspring stretchor compressionThe potential energy storedin a spring when it is ei-ther stretched or ,x= 0 corresponds tothe natural length of Harmonic MotionTs= 2 mkTs= period of motionk= spring constantm= attached massThe period of the simple har-monic motion of a massmat-tached to an ideal spring withspring 2 lgTp= period of motionl= pendulum lengthg= acceleration dueto gravityThe period of the simple har-monic motion of a massmonan ideal pendulum of 6 SAT Subject Physics Formula ReferenceGravityFg=Gm1m2r2Fg= force of gravityG= a constantm1, m2= massesr= distance ofseparationNewton s Law of Gravitation.

5 This formula gives the attrac-tive force between two massesa Fields and ForcesF=kq1q2r2F= electric forcek= a constantq1, q2= chargesr= distance ofseparation Coulomb s Law . This for-mula gives the force of attrac-tion or repulsion between twocharges a electric forceE= electric fieldq= chargeA chargeq, when placed in anelectric fieldE, will feel a forceon it, given by this formula(qis sometimes called a test charge, since it tests the elec-tric field strength).E=kqr2E= electric fieldk= a constantq= charger= distance ofseparationThis formula gives the elec-tric field due to a chargeqata distancerfrom the the test charge, thechargeqhere is actually gen-erating the electric 7 SAT Subject Physics Formula ReferenceElectric Fields and Forces (continued)UE=kq1q2rUE= electric PEk= a constantq1, q2= chargesr= distance ofseparationThis formula gives the elec-tric potential energy for twocharges a more than one pair ofcharges, use this formula foreach pair, then add all theUE s.

6 V= WEq= UEq V= potential differenceWE= work done by E fieldUE= electric PEq= chargeThe potential difference Vbetween two points is definedas the negative of the workdone by the electric field perunit charge as chargeqmovesfrom one point to the , it is the changein electric potential energy perunit electric potentialk= a constantq= charger= distance ofseparationThis formula gives the electricpotential due to a chargeqata distancerfrom the more than one charge, usethis formula for each charge,then add all theV electric fieldV= voltaged= distanceBetween two large plates ofmetal separated by a distancedwhich are connected to abattery of voltageV, a uni-form electric field between theplates is set up, as given bythis voltageI= currentR= resistance Ohm s Law . This law givesthe relationship between thebattery voltageV, the currentI, and the resistanceRin 8 SAT Subject Physics Formula ReferenceCircuits (continued)P=IVorP=V2/RorP=I2RP= powerI= currentV= voltageR= resistanceAll of these power formulasare equivalent and give thepower used in a circuit resistorR.

7 Use the formula that hasthe quantities that you +R2+..Rs= total (series)resistanceR1= first resistorR2= second resistor..When resistors are placed endto end, which is called in se-ries , the effective total resis-tance is just the sum of the in-dividual +1R2+..Rp= total (parallel)resistanceR1= first resistorR2= second resistor..When resistors are placed sideby side (or in parallel ), theeffective total resistance is theinverse of the sum of the re-ciprocals of the individual re-sistances (whew!).q=CVq= chargeC= capacitanceV= voltageThis formula is Ohm s Law for capacitors. Here,Cis anumber specific to the capac-itor (likeRfor resistors),qisthe charge on one side of thecapacitor, andVis the volt-age across the 9 SAT Subject Physics Formula ReferenceMagnetic Fields and ForcesF=ILBsin F= force on a wireI= current in the wireL= length of wireB= external magnetic field = angle between thecurrent direction andthe magnetic fieldThis formula gives the forceon a wire carrying currentIwhile immersed in a magneticfieldB.

8 Here, is the anglebetween the direction of thecurrent and the direction ofthe magnetic field ( is usu-ally 90 , so that the force isF=ILB).F=qvBsin F= force on a chargeq= chargev= velocity of the chargeB= external magnetic field = angle between thedirection of motion andthe magnetic fieldThe force on a chargeqas ittravels with velocityvthrougha magnetic fieldBis given bythis formula. Here, is theangle between the direction ofthe charge s velocity and thedirection of the magnetic field( is usually 90 , so that theforce isF=qvB).Waves and Opticsv= fv= wave velocity = wavelengthf= frequencyThis formula relates the wave-length and the frequency of awave to its speed. The for-mula works for both soundand light velocity of lightc= vacuum light speedn= index of refractionWhen light travels through amedium (say, glass), it slowsdown.

9 This formula gives thespeed of light in a mediumthat has an index of refractionn. Here,c= 108 10 SAT Subject Physics Formula ReferenceWaves and Optics (continued)n1sin 1=n2sin 2n1= incident index 1= incident anglen2= refracted index 2= refracted angle Snell s Law . When lightmoves from one medium (say,air) to another (say, glass)with a different index of re-fractionn, it changes direc-tion (refracts). The angles aretaken from the normal (per-pendicular).1do+1di=1fdo= object distancedi= image distancef= focal lengthThis formula works for lensesand mirrors, and relates thefocal length, object distance,and image didom= magnificationdi= image distancedo= object distanceThe magnificationmis howmuch bigger (|m|>1) orsmaller (|m|<1) the imageis compared to the object. Ifm <0, the image is invertedcompared to the and ThermodynamicsQ=mc TQ= heat addedor removedm= mass of substancec= specific heat T= change intemperatureThe specific heatcfor a sub-stance gives the heat neededto raise the temperature of amassmof that substance by Tdegrees.

10 If T <0, theformula gives the heat thathas to beremovedto lower 11 SAT Subject Physics Formula ReferenceHeat and Thermodynamics (continued)Q=mlQ= heat addedor removedm= mass of substancel= specific heatof transformationWhen a substance undergoesa change of phase (for exam-ple, when ice melts), the tem-perature doesn t change; how-ever, heat has to be added (icemelting) or removed (waterfreezing). The specific heatof transformationlis differentfor each substance. U=Q W U= change ininternal energyQ= heat addedW= work doneby the systemThe first law of thermody-namics . The change in inter-nal energy of a system is theheat added minus the workdone by the 100 Eeng= % efficiency ofthe heat engineW= work doneby the engineQhot= heat absorbedby the engineA heat engine essentially con-verts heat into work.