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 formula. Kinematics vave =averagevelocity ∆x The definition of average ve- vave = ∆x =displacement ∆t locity. ∆t =elapsedtime vave =averagevelocity (v + v ) Another definition of the av- v = i f ave 2 vi =initialvelocity erage velocity, which works a vf =finalvelocity when is constant. a =acceleration ∆v a = ∆t ∆v =changeinvelocity The definition of acceleration. ∆t =elapsedtime ∆x =displacement v 1 2 i =initialvelocity Use this formula when you ∆x = vi∆t + a(∆t) 2 ∆t =elapsedtime don’t have vf . a =acceleration ∆x =displacement vf =finalvelocity 1 2 Use this formula when you ∆x = vf ∆t − a(∆t) 2 ∆t =elapsedtime don’t have vi. a =acceleration www.erikthered.com/tutor pg. 1 SAT Subject Physics Formula Reference Kinematics (continued) vf =finalvelocity 2 2 vi =initialvelocity Use this formula when you vf = vi +2a∆x a =acceleration don’t have ∆t. ∆x =displacement Dynamics F =force Newton’s Second Law. Here, F = ma m =mass F is the net force on the mass a =acceleration m. W =weight The weight of an object with m W = mg =mass mass m.Thisisreallyjust g =accelerationdue Newton’s Second Law again. to gravity f =frictionforce The “Physics is Fun” equa- tion. Here, µ can be either µ =coefficient f = µN the kinetic coefficient of fric- of friction tion µ or the static coefficient N =normalforce k of friction µs. p =momentum The definition of momentum. p = mv m =mass It is conserved (constant) if there are no external forces on v =velocity asystem. www.erikthered.com/tutor pg. 2 SAT Subject Physics Formula Reference Dynamics (continued) ∆p =change in momentum ∆p = F ∆t F ∆t is called the impulse. F =appliedforce ∆t =elapsedtime Work, Energy, and Power W =work F =force W = Fdcos θ Work is done when a force d =distance is applied to an object as it or moves a distance d. F is the θ =anglebetweenF ! component of F in the direc- W = F!d and the direction tion that the object is moved. of motion F! =parallelforce KE = kinetic energy 1 The definition of kinetic en- KE = mv2 2 m =mass ergy for a mass m with veloc- v =velocity ity v. PE = potential energy m =mass The potential energy for a PE = mgh g =accelerationdue mass m at a height h above to gravity some reference level. h =height www.erikthered.com/tutor pg. 3 SAT Subject Physics Formula Reference Work, Energy, Power (continued) The “work-energy” theorem: W W =∆(KE) =workdone the work done by the net force KE = kinetic energy on an object equals the change in kinetic energy of the object. E=totalenergy The definition of total (“me- chanical”) energy. If there E=KE+PE KE = kinetic energy is no friction, it is conserved PE = potential energy (stays constant). P =power Power is the amount of work W P = W =work done per unit time (i.e., power ∆t is the rate at which work is ∆t =elapsedtime done). Circular Motion The “centripetal” acceleration 2 ac =centripetalacceleration v for an object moving around ac = v =velocity r in a circle of radius r at veloc- r =radius ity v. Fc =centripetalforce The “centripetal” force that is 2 mv m =mass needed to keep an object of Fc = r v =velocity mass m moving around in a circle of radius r at velocity v. r =radius www.erikthered.com/tutor pg. 4 SAT Subject Physics Formula Reference Circular Motion (continued) v =velocity This formula gives the veloc- 2πr v = r =radius ity v of an object moving once T around a circle of radius r in T =period time T (the period). 1 f =frequency The frequency is the number f = of times per second that an T T =period object moves around a circle. Torques and Angular Momentum τ =torque τ = rF sin θ r =distance(radius) Torque is a force applied at a distance r from the axis of ro- or F =force tation. F⊥ = F sin θ is the θ F τ = rF⊥ =anglebetween component of F perpendicu- and the lever arm lar to the lever arm. F⊥ =perpendicularforce L =angularmomentum Angular momentum is con- m =mass served (i.e., it stays constant) L = mvr v =velocity as long as there are no exter- nal torques. r =radius www.erikthered.com/tutor pg. 5 SAT Subject Physics Formula Reference Springs Fs =springforce “Hooke’s Law”. The force is k =springconstant Fs = kx opposite to the stretch or com- x =springstretchor pression direction. compression The potential energy stored PEs =potentialenergy in a spring when it is ei- k =springconstant 1 2 ther stretched or compressed. PEs = kx 2 x =amountof Here, x =0correspondsto spring stretch the “natural length” of the or compression spring. Gravity Fg =forceofgravity Newton’s Law of Gravitation: G =aconstant m1m2 this formula gives the attrac- Fg = G 2 r m1,m2 =masses tive force between two masses r =distanceof adistancer apart. separation Electric Fields and Forces Fe =electricforce “Coulomb’s Law”. This for- k =aconstant q1q2 mula gives the force of attrac- Fe = k 2 r q1,q2 =charges tion or repulsion between two r =distanceof charges a distance r apart. separation www.erikthered.com/tutor pg. 6 SAT Subject Physics Formula Reference Electric Fields and Forces (continued) Achargeq,whenplacedinan F =electricforce electric field E,willfeelaforce F = qE E =electricfield on it, given by this formula (q is sometimes called a “test” q =charge charge, since it tests the elec- tric field strength). E =electricfield This formula gives the elec- k =aconstant tric field due to a charge q at q adistancer from the charge. E = k 2 q =charge r Unlike the “test” charge, the r =distanceof charge q here is actually gen- separation erating the electric field. Between two large plates of metal separated by a distance E =electricfield V d which are connected to a E = V =voltage d battery of voltage V ,auni- d =distance form electric field between the plates is set up, as given by this formula. The potential difference ∆V ∆V =potentialdifference between two points (say, the W terminals of a battery), is de- ∆V = W =work q fined as the work per unit q =charge charge needed to move charge q from one point to the other. Circuits “Ohm’s Law”. This law gives V =voltage the relationship between the V = IR I =current battery voltage V ,thecurrent R =resistance I,andtheresistanceR in a circuit. www.erikthered.com/tutor pg. 7 SAT Subject Physics Formula Reference Circuits (continued) P = IV P =power All of these power formulas or are equivalent and give the 2 I =current P = V /R power used in a circuit resistor V =voltage or R.Usetheformulathathas R =resistance the quantities that you know. P = I2R Rs =total(series) When resistors are placed end resistance to end, which is called “in se- Rs = R1 =firstresistor ries”, the effective total resis- R1 + R2 + ... R2 =secondresistor tance is just the sum of the in- ... dividual resistances. When resistors are placed side 1 Rp =total(parallel) = resistance by side (or “in parallel”), the Rp effective total resistance is the R1 =firstresistor inverse of the sum of the re- 1 1 R2 =secondresistor + + ... ciprocals of the individual re- R1 R2 ... sistances (whew!). This formula is “Ohm’s Law” for capacitors. Here, C is a q =charge number specific to the capac- q = CV C =capacitance itor (like R for resistors), q is V =voltage the charge on one side of the capacitor, and V is the volt- age across the capacitor. www.erikthered.com/tutor pg. 8 SAT Subject Physics Formula Reference Magnetic Fields and Forces This formula gives the force F =forceonawire on a wire carrying current I I =currentinthewire while immersed in a magnetic L =lengthofwire field B.Here,θ is the angle F = ILB sin θ between the direction of the B =externalmagneticfield current and the direction of θ =anglebetweenthe the magnetic field (θ is usu- current direction and ally 90◦,sothattheforceis the magnetic field F = ILB). The force on a charge q as it F =forceonacharge travels with velocity v through q =charge amagneticfieldB is given by v =velocityofthecharge this formula. Here, θ is the F = qvB sin θ angle between the direction of B =externalmagneticfield the charge’s velocity and the θ =anglebetweenthe direction of the magnetic field direction of motion and (θ is usually 90◦,sothatthe the magnetic field force is F = qvB). Waves and Optics This formula relates the wave- v =wavevelocity length and the frequency of a v = λf λ =wavelength wave to its speed. The for- f =frequency mula works for both sound and light waves. When light travels through a v =velocityoflight medium (say, glass), it slows c down. This formula gives the v = c =vacuumlightspeed n speed of light in a medium n =indexofrefraction that has an index of refraction n.Here,c =3.0 × 108 m/s. www.erikthered.com/tutor pg. 9 SAT Subject Physics Formula Reference Waves and Optics (continued) “Snell’s Law”. When light moves from one medium (say, n1 =incidentindex air) to another (say, glass) θ1 =incidentangle with a different index of re- n1 sin θ1 = n2 sin θ2 n2 =refractedindex fraction n,itchangesdirec- tion (refracts). The angles are θ2 =refractedangle taken from the normal (per- pendicular).