Kinematics

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 are not given 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 formula.Kinematicsvave x tvave average velocity x displacementThe definition of average velocity. t elapsed timevave(vi vf ) 2vave average velocityvi initial velocityvf final velocitya v tAnother definition of the average velocity, which workswhen a is constant.a acceleration v change in velocityThe definition of acceleration. t elapsed time x displacement1 x vi t a( t)22vi initial velocity t elapsed timeUse this formula when youdon’t have vf .a acceleration x displacement1 x vf t a( t)22vf final velocity t elapsed timeUse this formula when youdon’t have vi .a accelerationwww.erikthered.com/tutorpg. 1

SAT Subject Physics Formula ReferenceKinematics (continued)vf final velocityvf2 vi2 2a xvi initial velocitya accelerationUse this formula when youdon’t have t. x displacementDynamicsF forceF mam massa accelerationW weightW mgm massg acceleration dueto gravityf friction forcef µNµ coefficientof frictionN normal forcep momentump mvm massv velocitywww.erikthered.com/tutorNewton’s Second Law. Here,F is the net force on the massm.The weight of an object withmass m. This is really justNewton’s Second Law again.The “Physics is Fun” equation. Here, µ can be eitherthe kinetic coefficient of friction µk or the static coefficientof friction µs .The definition of momentum.It is conserved (constant) ifthere are no external forces ona system.pg. 2

SAT Subject Physics Formula ReferenceDynamics (continued) p F t p changein momentumF applied forceF t is called the impulse. t elapsed timeWork, Energy, and PowerW workW F d cos θorW F! d1KE mv 22F forced distanceθ angle between Fand the directionof motionF! parallel forceKE kinetic energym massv velocityWork is done when a forceis applied to an object as itmoves a distance d. F! is thecomponent of F in the direction that the object is moved.The definition of kinetic energy for a mass m with velocity v.PE potential energym massPE mghg acceleration dueto gravityThe potential energy for amass m at a height h abovesome reference level.h heightwww.erikthered.com/tutorpg. 3

SAT Subject Physics Formula ReferenceWork, Energy, Power (continued)W (KE)W work doneKE kinetic energyE total energyE KE PEKE kinetic energyPE potential energyP powerWP tW work t elapsed timeThe “work-energy” theorem:the work done by the net forceon an object equals the changein kinetic energy of the object.The definition of total (“mechanical”) energy. If thereis no friction, it is conserved(stays constant).Power is the amount of workdone per unit time (i.e., poweris the rate at which work isdone).Circular Motionac centripetal accelerationv2ac rv velocityr radiusFc centripetal forcemvFc r2m massv velocityr radiuswww.erikthered.com/tutorThe “centripetal” accelerationfor an object moving aroundin a circle of radius r at velocity v.The “centripetal” force that isneeded to keep an object ofmass m moving around in acircle of radius r at velocity v.pg. 4

SAT Subject Physics Formula ReferenceCircular Motion (continued)v velocity2πrv Tf r radiusT periodf frequency1TT periodThis formula gives the velocity v of an object moving oncearound a circle of radius r intime T (the period).The frequency is the numberof times per second that anobject moves around a circle.Torques and Angular Momentumτ torqueτ rF sin θorτ rF r distance (radius)F forceθ angle between Fand the lever armF perpendicular forceL angular momentumL mvrm massv velocityr radiuswww.erikthered.com/tutorTorque is a force applied at adistance r from the axis of rotation. F F sin θ is thecomponent of F perpendicular to the lever arm.Angular momentum is conserved (i.e., it stays constant)as long as there are no external torques.pg. 5

SAT Subject Physics Formula ReferenceSpringsFs spring forceFs kxk spring constantx spring stretch orcompressionPEs potential energyPEs 1 2kx2k spring constantx amount ofspring stretchor compression“Hooke’s Law”. The force isopposite to the stretch or compression direction.The potential energy storedin a spring when it is either stretched or compressed.Here, x 0 corresponds tothe “natural length” of thespring.GravityFg force of gravitym1 m2Fg G 2rG a constantm1 , m2 massesr distance ofseparationNewton’s Law of Gravitation:this formula gives the attractive force between two massesa distance r apart.Electric Fields and ForcesFe electric forceq1 q2Fe k 2rk a constantq1 , q2 chargesr distance ofseparationwww.erikthered.com/tutor“Coulomb’s Law”. This formula gives the force of attraction or repulsion between twocharges a distance r apart.pg. 6

SAT Subject Physics Formula ReferenceElectric Fields and Forces (continued)F electric forceF qEE electric fieldq chargeE electric fieldE kqr2k a constantq charger distance ofseparationVE d V WqE electric fieldV voltaged distance V potential differenceW workq chargeA charge q, when placed in anelectric field E, will feel a forceon it, given by this formula(q is sometimes called a “test”charge, since it tests the electric field strength).This formula gives the electric field due to a charge q ata distance r from the charge.Unlike the “test” charge, thecharge q here is actually generating the electric field.Between two large plates ofmetal separated by a distanced which are connected to abattery of voltage V , a uniform electric field between theplates is set up, as given bythis formula.The potential difference Vbetween two points (say, theterminals of a battery), is defined as the work per unitcharge needed to move chargeq from one point to the other.CircuitsV voltageV IRI currentR resistancewww.erikthered.com/tutor“Ohm’s Law”. This law givesthe relationship between thebattery voltage V , the currentI, and the resistance R in acircuit.pg. 7

SAT Subject Physics Formula ReferenceCircuits (continued)P IVorP V 2 /RorP I 2RRs R1 R2 . . .P powerI currentV voltageR resistanceRs total (series)resistanceR1 first resistorR2 second resistor.1 RpRp total (parallel)resistanceR1 first resistor11 .R1R2R2 second resistor.q chargeq CVC capacitanceV voltagewww.erikthered.com/tutorAll of these power formulasare equivalent and give thepower used in a circuit resistorR. Use the formula that hasthe quantities that you know.When resistors are placed endto end, which is called “in series”, the effective total resistance is just the sum of the individual resistances.When resistors are placed sideby side (or “in parallel”), theeffective total resistance is theinverse of the sum of the reciprocals of the individual resistances (whew!).This formula is “Ohm’s Law”for capacitors. Here, C is anumber specific to the capacitor (like R for resistors), q isthe charge on one side of thecapacitor, and V is the voltage across the capacitor.pg. 8

SAT Subject Physics Formula ReferenceMagnetic Fields and ForcesF force on a wireI current in the wireL length of wireF ILB sin θB external magnetic fieldθ angle between thecurrent direction andthe magnetic fieldF force on a chargeq chargeF qvB sin θv velocity of the chargeB external magnetic fieldθ angle between thedirection of motion andthe magnetic fieldThis formula gives the forceon a wire carrying current Iwhile immersed in a magneticfield B. Here, θ is the anglebetween the direction of thecurrent and the direction ofthe magnetic field (θ is usually 90 , so that the force isF ILB).The force on a charge q as ittravels with velocity v througha magnetic field B is given bythis formula. Here, θ is theangle between the direction ofthe charge’s velocity and thedirection of the magnetic field(θ is usually 90 , so that theforce is F qvB).Waves and Opticsv wave velocityv λfλ wavelengthf frequencyv cnv velocity of lightc vacuum light speedn index of refractionwww.erikthered.com/tutorThis formula relates the wavelength and the frequency of awave to its speed. The formula works for both soundand light waves.When light travels through amedium (say, glass), it slowsdown. This formula gives thespeed of light in a mediumthat has an index of refractionn. Here, c 3.0 108 m/s.pg. 9

SAT Subject Physics Formula ReferenceWaves and Optics (continued)n1 incident indexn1 sin θ1 n2 sin θ2θ1 incident anglen2 refracted indexθ2 refracted angle111 dodifdo object distancedi image distancef focal lengthm didom magnificationdi image distancedo object distance“Snell’s Law”. When lightmoves from one medium (say,air) to another (say, glass)with a different index of refraction n, it changes direction (refracts). The angles aretaken from the normal (perpendicular).This formula works for lensesand mirrors, and relates thefocal length, object distance,and image distance.The magnification m is howmuch bigger ( m 1) orsmaller ( m 1) the imageis compared to the object. Ifm 0, the image is invertedcompared to the object.Heat and ThermodynamicsQ mc TQ heat addedor removedm mass of substancec specific heat T change intemperaturewww.erikthered.com/tutorThe specific heat c for a substance gives the heat neededto raise the temperature of amass m of that substance by T degrees. If T 0, theformula gives the heat thathas to be removed to lower thetemperature.pg. 10

SAT Subject Physics Formula ReferenceHeat and Thermodynamics (continued)Q mlQ heat addedor removedm mass of substancel specific heatof transformation U change ininternal energy U Q WQ heat addedW work doneby the systemEeng W 100QhotEeng % efficiency ofthe heat engineW work doneby the engineQhot heat absorbedby the engineWhen a substance undergoesa change of phase (for example, when ice melts), the temperature doesn’t change; however, heat has to be added (icemelting) or removed (waterfreezing). The specific heatof transformation l is differentfor each substance.The “first law of thermodynamics”. The change in internal energy of a system is theheat added minus the workdone by the system.A heat engine essentially converts heat into work. Theengine does work by absorbing heat from a hot reservoirand discarding some heat toa cold reservoir. The formulagives the quality (“efficiency”)of the engine.Pressure and GasesFP Awww.erikthered.com/tutorP pressureF forceA areaThe definition of pressure. Pis a force per unit area exertedby a gas or fluid on the wallsof the container.pg. 11

SAT Subject Physics Formula ReferencePressure and Gases (continued)P pressurePV constantTV volumeT temperatureThe “Ideal Gas Law”. For“ideal” gases (and also forreal-life gases at low pressure),the pressure of the gas timesthe volume of the gas dividedby the temperature of the gasis a constant.Modern Physics and RelativityE photon energyE hfh a constantf wave frequencyλ hpλ matter wavelengthh a constantp momentumγ !11 (v/c)2www.erikthered.com/tutorγ the relativistic factorv speed of movingobserverc speed of lightThe energy of a photon isproportional to its wave frequency; h is a number called“Planck’s constant”.A particle can act like a wavewith wavelength λ, as given bythis formula, if it has momentum p. This is called “waveparticle” duality.The relativistic factor γ isthe amount by which movingclocks slow down and lengthscontract, as seen by an observer compared to those ofanother observer moving atspeed v (note that γ 1).pg. 12

SAT Subject Physics Formula Reference This guide is a compilation of about fifty of the most importantphysicsformulastoknow for the SAT Subject test in physics. (Note that formulas are not given on the test.) Each formula row contains a description of the variables or constants that make up the formula, along with a brief explanation of the .