Formula sheet for physics, Cheat Sheet of Physics

Download Formula sheet for physics and more Cheat Sheet Physics in PDF only on Docsity! SAT Subject Physics Formula Reference This guide is a compilation of about fifty of the most important physics formulas to know 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 = !x !t vave = average velocity !x = displacement !t = elapsed time The definition of average ve- locity. vave = (vi + vf) 2 vave = average velocity vi = initial velocity vf = final velocity Another definition of the av- erage velocity, which works when a is constant. a = !v !t a = acceleration !v = change in velocity !t = elapsed time The definition of acceleration. !x = vi!t + 1 2 a(!t)2 !x = displacement vi = initial velocity !t = elapsed time a = acceleration Use this formula when you don’t have vf . !x = vf!t ! 1 2 a(!t)2 !x = displacement vf = final velocity !t = elapsed time a = acceleration Use this formula when you don’t have vi. www.erikthered.com/tutor pg. 1 SAT Subject Physics Formula Reference Kinematics (continued) v2 f = v2 i + 2a!x vf = final velocity vi = initial velocity a = acceleration !x = displacement Use this formula when you don’t have !t. Dynamics F = ma F = force m = mass a = acceleration Newton’s Second Law. Here, F is the net force on the mass m. W = mg W = weight m = mass g = acceleration due to gravity The weight of an object with mass m. This is really just Newton’s Second Law again. f = µN f = friction force µ = coe"cient of friction N = normal force The “Physics is Fun” equa- tion. Here, µ can be either the kinetic coe"cient of fric- tion µk or the static coe"cient of friction µs. p = mv p = momentum m = mass v = velocity The definition of momentum. It is conserved (constant) if there are no external forces on a system. www.erikthered.com/tutor pg. 2 SAT Subject Physics Formula Reference Circular Motion (continued) v = 2"r T v = velocity r = radius T = period This formula gives the veloc- ity v of an object moving once around a circle of radius r in time T (the period). f = 1 T f = frequency T = period The frequency is the number of times per second that an object moves around a circle. Torques and Angular Momentum # = rF sin ! or # = rF" " = torque r = distance (radius) F = force ! = angle between F and the lever arm F" = perpendicular force Torque is a force applied at a distance r from the axis of ro- tation. F" = F sin ! is the component of F perpendicu- lar to the lever arm. L = mvr L = angular momentum m = mass v = velocity r = radius Angular momentum is con- served (i.e., it stays constant) as long as there are no exter- nal torques. www.erikthered.com/tutor pg. 5 SAT Subject Physics Formula Reference Springs Fs = kx Fs = spring force k = spring constant x = spring stretch or compression “Hooke’s Law”. The force is opposite to the stretch or com- pression direction. PEs = 1 2 kx2 PEs = potential energy k = spring constant x = amount of spring stretch or compression The potential energy stored in a spring when it is ei- ther stretched or compressed. Here, x = 0 corresponds to the “natural length” of the spring. Gravity Fg = G m1m2 r2 Fg = force of gravity G = a constant m1, m2 = masses r = distance of separation Newton’s Law of Gravitation: this formula gives the attrac- tive force between two masses a distance r apart. Electric Fields and Forces Fe = k q1q2 r2 Fe = electric force k = a constant q1, q2 = charges r = distance of separation “Coulomb’s Law”. This for- mula gives the force of attrac- tion or repulsion between two charges a distance r apart. www.erikthered.com/tutor pg. 6 SAT Subject Physics Formula Reference Electric Fields and Forces (continued) F = qE F = electric force E = electric field q = charge A charge q, when placed in an electric field E, will feel a force on it, given by this formula (q is sometimes called a “test” charge, since it tests the elec- tric field strength). E = k q r2 E = electric field k = a constant q = charge r = distance of separation This formula gives the elec- tric field due to a charge q at a distance r from the charge. Unlike the “test” charge, the charge q here is actually gen- erating the electric field. E = V d E = electric field V = voltage d = distance Between two large plates of metal separated by a distance d which are connected to a battery of voltage V , a uni- form electric field between the plates is set up, as given by this formula. !V = W q !V = potential di#erence W = work q = charge The potential di#erence !V between two points (say, the terminals of a battery), is de- fined as the work per unit charge needed to move charge q from one point to the other. Circuits V = IR V = voltage I = current R = resistance “Ohm’s Law”. This law gives the relationship between the battery voltage V , the current I, and the resistance R in a circuit. www.erikthered.com/tutor pg. 7 SAT Subject Physics Formula Reference Waves and Optics (continued) n1 sin !1 = n2 sin !2 n1 = incident index !1 = incident angle n2 = refracted index !2 = refracted angle “Snell’s Law”. When light moves from one medium (say, air) to another (say, glass) with a di#erent index of re- fraction n, it changes direc- tion (refracts). The angles are taken from the normal (per- pendicular). 1 do + 1 di = 1 f do = object distance di = image distance f = focal length This formula works for lenses and mirrors, and relates the focal length, object distance, and image distance. m = ! di do m = magnification di = image distance do = object distance The magnification m is how much bigger (|m| > 1) or smaller (|m| < 1) the image is compared to the object. If m < 0, the image is inverted compared to the object. Heat and Thermodynamics Q = mc !T Q = heat added or removed m = mass of substance c = specific heat !T = change in temperature The specific heat c for a sub- stance gives the heat needed to raise the temperature of a mass m of that substance by !T degrees. If !T < 0, the formula gives the heat that has to be removed to lower the temperature. www.erikthered.com/tutor pg. 10 SAT Subject Physics Formula Reference Heat and Thermodynamics (continued) Q = ml Q = heat added or removed m = mass of substance l = specific heat of transformation When a substance undergoes a change of phase (for exam- ple, when ice melts), the tem- perature doesn’t change; how- ever, heat has to be added (ice melting) or removed (water freezing). The specific heat of transformation l is di#erent for each substance. !U = Q ! W !U = change in internal energy Q = heat added W = work done by the system The “first law of thermody- namics”. The change in inter- nal energy of a system is the heat added minus the work done by the system. Eeng = W Qhot " 100 Eeng = % e"ciency of the heat engine W = work done by the engine Qhot = heat absorbed by the engine A heat engine essentially con- verts heat into work. The engine does work by absorb- ing heat from a hot reservoir and discarding some heat to a cold reservoir. The formula gives the quality (“e"ciency”) of the engine. Pressure and Gases P = F A P = pressure F = force A = area The definition of pressure. P is a force per unit area exerted by a gas or fluid on the walls of the container. www.erikthered.com/tutor pg. 11 SAT Subject Physics Formula Reference Pressure and Gases (continued) PV T = constant P = pressure V = volume T = temperature The “Ideal Gas Law”. For “ideal” gases (and also for real-life gases at low pressure), the pressure of the gas times the volume of the gas divided by the temperature of the gas is a constant. Modern Physics and Relativity E = hf E = photon energy h = a constant f = wave frequency The energy of a photon is proportional to its wave fre- quency; h is a number called “Planck’s constant”. $ = h p # = matter wavelength h = a constant p = momentum A particle can act like a wave with wavelength #, as given by this formula, if it has momen- tum p. This is called “wave- particle” duality. % = 1 ! 1 ! (v/c)2 $ = the relativistic factor v = speed of moving observer c = speed of light The relativistic factor $ is the amount by which moving clocks slow down and lengths contract, as seen by an ob- server compared to those of another observer moving at speed v (note that $ " 1). www.erikthered.com/tutor pg. 12