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Table forfor APAP Physics C Exams Table of of Information Informationand andEquation EquationTables Tables Physics Exams The accompanying Table The accompanying Table of ofInformation Informationand andEquation EquationTables Tableswill willbebeprovided providedtotostudents studentswhen when they take the AP Physics C Exams. Therefore, students may NOT bring their own copies of these they take the AP Physics Exams. Therefore, students may NOT bring their own copies of these tables to the exam room, although they may use them throughout the year in their classes in tables to the exam room, although they may use them throughout the year in their classes in order to become familiar with their content. Check the Physics course home pages on AP order to become familiar with their content. Check the Physics course home pages on AP Central for the latest versions of these tables (apcentral.collegeboard.org). Central for the latest versions of these tables (apcentral.collegeboard.org). Table of Information Table of the Information For both Physics C: Mechanics and Physics C: Electricity and Magnetism Exams, the Table of For both the and the Physics Exams, the Table of Information is printed near the front Information isPhysics printedBnear frontCcover of both the multiple-choice and free-response sections. cover of both multiple-choice and free-response sections. The tables are identical for both The tables arethe identical for both exams. exams except for one convention as noted. Equation Tables For both the Physics C: Mechanics and Physics C: Electricity and Magnetism Exams, the Equation Tables equation tables for each exam are printed near the theequation front cover of both the multiple-choice andnear For both the Physics B and Physics C Exams, tables for each exam are printed free-response directly following theonly, tabledirectly of information. The may be The the front coversections, of the free-response section following theequation table oftables information. used by students when taking both the multiple-choice and free-response sections of both exams. equation tables may be used by students when taking the free-response sections of both exams The equations in the tables express the relationships that are encountered most frequently in but NOT when taking the multiple-choice sections. AP Physic C courses and exams. However, the tables do not include all equations that might The equations in the tables express the relationships that are encountered most frequently in possibly be used. For example, they do not include many equations that can be derived by AP Physics courses and exams. However, the tables do not include all equations that might combining other equations in the tables. Nor do they include equations that are simply special possibly be used. Forinexample, they do notare include many equations that can be by cases of any that are the tables. Students responsible for understanding thederived physical combining other equations in the tables. Nor do they include equations that are simply special principles that underlie each equation and for knowing the conditions for which each equation cases of any that are in the tables. Students are responsible for understanding the physical is applicable. principles that underlie equationinand for knowing thetoconditions whichcategory each equation is The equation tables each are grouped sections according the majorfor content in which applicable. they appear. Within each section, the symbols used for the variables in that section are defined. However, in sometables casesare thegrouped same symbol is used to represent quantities in different The equation in sections according to thedifferent major content category in which tables. It should be noted therethe is symbols no uniform convention among textbooks for the they appear. Within each that section, used for the variables in that section aresymbols defined. used in writing equations. The equation tables follow many common conventions, in some However, in some cases the same symbol is used to represent different quantities but in different cases was sacrificed for the sake of clarity. tables.consistency It should be noted that there is no uniform convention among textbooks for the symbols usedSome explanations about notation used in equation tables: in writing equations. The equation tablesthe follow many common conventions, but in some 1. The symbols used for physical constants are the same as those in the Table of cases consistency was sacrificed for the sake of clarity. Information and are defined in the Table of Information rather than in the right-hand Some explanations about notation used in the equation tables: columns of the tables. 1. The symbols used for physical constants are the same as those in the Table of 2.Symbols with arrows above them represent vector quantities. Information and are defined the Tableare of used Information ratherspecial than incases the right-hand 3. Subscripts on symbols in theinequations to represent of the columns the tables. variablesof defined in the right-hand columns. 2. Symbols in bold face represent quantities. D before 4.The symbol a variable vector in an equation specifically indicates a change in the 3. Subscripts on final symbols the equations are used to represent special cases of the variable (i.e., valueinminus initial value). variables defined symbols in the right-hand 5. Several different (e.g., d, r,columns. s, h, ) are used for linear dimensions such as length. The particular used in equation an equation is one that is commonly usedinfor 4. The symbol D before asymbol variable in an specifically indicates a change the that equation in textbooks. variable (i.e., final value minus initial value). 5. Several different symbols (e.g., d, r, s, h, A ) are used for linear dimensions such as length. The particular symbol used in an equation is one that is commonly used for that equation in textbooks. © 2014 The College Board. Visit the College Board on the Web: www.collegeboard.org. ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS m p 1.67 ¥ 10 -27 kg Proton mass, = e 1.60 ¥ 10 -19 C Electron charge magnitude, = Neutron mass, = mn 1.67 ¥ 10 -27 kg eV 1.60 ¥ 10 -19 J 1 electron volt, 1= Electron mass, = me 9.11 ¥ 10 -31 kg Avogadro’s number, = N 0 6.02 ¥ 10 23 mol -1 R = 8.31 J (mol K) Universal gas constant, Speed of light, = c 3.00 ¥ 108 m s Universal gravitational = G 6.67 ¥ 10 -11 Nm 2 constant, Acceleration due to gravity g = 9.8 m s2 at Earth’s surface, ( ) kg 2 Boltzmann’s constant, = k B 1.38 ¥ 10 -23 J K 1u = 1.66 ¥ 10 -27 kg = 931 MeV c 2 1 unified atomic mass unit, h= 6.63 ¥ 10 -34 J s = 4.14 ¥ 10 -15 eV s Planck’s constant, hc =¥ 1.99 10 -25 J m =¥ 1.24 103 eV nm ( = e0 8.85 ¥ 10 -12 C2 N m 2 Vacuum permittivity, ( k 1 ( 4 pe= 9.0 ¥ 109 N m 2 Coulomb’s law constant, = 0) ) ) C2 m= 4 p ¥ 10 -7 (T m) A 0 Vacuum permeability, Magnetic constant, k ¢= m0 ( 4 p )= 1 ¥ 10 -7 (T m) A 1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa 1 atmosphere pressure, UNIT SYMBOLS meter, kilogram, second, ampere, kelvin, PREFIXES Factor Prefix Symbol m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J watt, coulomb, volt, ohm, henry, W C V W H farad, tesla, degree Celsius, electron volt, F T ∞C eV VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q 30 0 37 45 53 60 90 10 9 giga G sin q 0 12 35 2 2 45 3 2 1 106 mega M cosq 1 3 2 45 2 2 35 12 0 103 kilo k tan q 0 3 3 34 1 43 3 • 10 -2 centi c -3 milli m -6 micro m 10 -9 nano n 10 -12 pico p 10 10 The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges would drift. III. The electric potential is zero at an infinite distance from an isolated point charge. IV. All batteries and meters are ideal unless otherwise stated. V. Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated. © 2014 The College Board. Visit the College Board on the Web: www.collegeboard.org. ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS = Ãx Ãx 0 + a x t 1 2 at 2 x x =x0 + Ãx 0 t + Ãx2 =Ãx 0 + 2 ax ( x - x0 ) a = 2 Fnet F  = m m dp F = dt = J Ú= F dt Dp p = mv F f £ m FN D= E W = K = Ú F dr 1 2 mà 2 dE dt P = F v P= DUg = mg Dh à a= = w2r c r t= r ¥ F t net Ât = a = I I r dm Ú= 2 x cm = 1 2 Us = k ( Dx ) 2 = x xmax cos( wt + f)  mr 2  mi xi  mi à = rw L = r ¥ p = Iw K = 1 2 Iw 2 2p = w 1 f Ts = 2 p m k Tp = 2p g = T Gm1m2 FG = r2 UG = - = w w0 + at q = q0 + w0 t + acceleration energy force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration phase angle Fs = - k D x 2 = I a = E= F = f = h = I = J = K = k = = L = m= P = p = r = T = t = U= v = W= x = m = q = t = w = a = f = ELECTRICITY AND MAGNETISM 1 2 at 2 Gm1m2 r FE = 1 q1q2 4pe0 r 2 FE E = q e Q Ú E dA = e0 F I J L n dV dx DV = - Ú E dr Ex = - 1 q1q2 4 pe0 r U= qV = E Q C DV = k e0 A d C =  Ci Cp = i 1 1 = Cs C i i I = dQ dt 1 = QDV 2 r R= A E = rJ = UC DV R Rs =  Ri 1 = Rp i 1 ÂR i = = = = = = = V= v = r = F= k = P Q q R r t U area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance radius or distance time potential or stored energy electric potential velocity or speed resistivity flux dielectric constant FM = qv ¥ B Ú B d = m0 I m I d ¥ r 0 1 C ( DV )2 dB = 4 p r2 2 = F Ú I d ¥ B I = Nevd A I = = = = = = = = = = = = = N = q  rii i 1 V = 4pe0 A B C d E i P = I DV © 2014 The College Board. Visit the College Board on the Web: www.collegeboard.org. Bs = m0 nI FB = Ú B dA dF E Ú d = - dt B e = e = -L UL = dI dt 1 2 LI 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle A= 1 bh 2 Circle A = pr2 C = 2p r s = rq Rectangular Solid V = wh Cylinder 2 V = pr CALCULUS df d f du = dx du dx A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius s = arc length q = angle d n ( x ) = nxn -1 dx d ax (e ) = aeax dx d ( ln ax ) = 1 dx x d [sin (ax )] = a cos (ax ) dx d [cos (ax )] = - a sin (ax ) dx s n = Ú x dx r q Úe = S 2p r + 2p r 2 Sphere dx ln x + a 1 Ú sin (ax) dx = Right Triangle a 2 + b2 = c2 tan q = 1 ax e a Ú cos (ax) dx = a sin (ax) S = 4p r 2 a c b cos q = c dx = Ú x += a 4 V = pr3 3 sin q = ax 1 n +1 x , n π -1 n +1 c q a 90 1 - cos (ax ) a VECTOR PRODUCTS A B = AB cos q A¥B = AB sin q b a b © 2014 The College Board. Visit the College Board on the Web: www.collegeboard.org.
