Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 1 of 8 #20 Heating a Solid, Liquid or Gas #3 Components of a Vector Q = mcT (no phase changes!) if V = 34 m/sec 48 Q = the heat added then c = specific heat. Vi = 34 m/sec(cos 48); and VJ = 34 m/sec(sin 48) T = temperature change, K #21 Linear Momentum #4 Weight = mg momentum = p = mv = mass velocity g = 9.81m/sec near the surface of the Earth momentum is conserved in collisions = 9.795 m/sec in Fort Worth, TX #23 Center of Mass point masses on a line Density = mass / volume xcm = (mx) / Mtotal = m V ( unit : kg / m 3 ) #25 Angular Speed vs. Linear Speed Linear speed = v = r = r angular speed #7 Ave speed = distance / time = v = d/t Ave velocity = displacement / time = v = d/t #26 Pressure under Water Ave acceleration = change in velocity / time P = gh h = depth of water #8 Friction Force = density of water FF = FN #28 Universal Gravitation If the object is not moving, you are dealing with static m1 m2 friction and it can have any value from zero up to s FN F =G If the object is sliding, then you are dealing with kinetic r2 friction and it will be constant and equal to K FN G = 6.67 E-11 N m / kg #9 Torque #29 Mechanical Energy PEGrav = P = mgh = FLsin KELinear = K = mv Where is the angle between F and L; unit: Nm #30 Impulse = Change in Momentum #11 Newton's Second Law Ft = (mv) Fnet = FExt = ma #31 Snell's Law #12 Work = FDcos n1sin 1 = n2sin 2 Where D is the distance moved and Index of Refraction is the angle between F and the n=c/v direction of motion, c = speed of light = 3 E+8 m/s unit : J #32 Ideal Gas Law #16 Power = rate of work done PV = nRT Work n = # of moles of gas Power = unit : watt R = gas law constant time = 8.31 J / K mole. Efficiency = Workout / Energyin #34 Periodic Waves Mechanical Advantage = force out / force in v = f M.A. = Fout / Fin f=1/T T = period of wave #19 Constant-Acceleration Linear Motion #35 Constant-Acceleration Circular Motion v = v + at x = + t (x-x) = vt + at v -= t + t 2 2 v = v + 2a (x - x) t = + 2(-) t (x-x) = ( v + v) t a - = ( + )t (x-x) = vt - at v - = t - t Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 2 of 8 #53 Resistor Combinations #36 Buoyant Force - Buoyancy SERIES FB = Vg = mDisplaced fluidg = weightDisplaced fluid Req = R1 + R2+ R3+. . . = density of the fluid PARALLEL n V = volume of fluid displaced 1 1 1 1 1 R eq = + R1 R 2 +K + Rn = R i =1 i #37 Ohm's Law V = IR #54 Newton's Second Law and V = voltage applied Rotational Inertia I = current = torque = I R = resistance I = moment of inertia = mr (for a point mass) (See table in Lesson 58 for I of 3D shapes.) Resistance of a Wire R = L / Ax #55 Circular Unbanked Tracks = resistivity of wire material mv 2 L = length of the wire = mg Ax = cross-sectional area of the wire r #56 Continuity of Fluid Flow #39 Heat of a Phase Change Ainvin = Aoutvout A= Area Q = mL v = velocity L = Latent Heat of phase change #58 Moment of Inertia - I cylindrical hoop mr2 #41 Hooke's Law solid cylinder or disk mr2 2 F = kx solid sphere /5 mr2 Potential Energy of a spring hollow sphere mr2 1 W = kx = Work done on spring thin rod (center) /12 mL2 thin rod (end) mL2 #42 Electric Power P = IR = V / R = IV #59 Capacitors Q = CV Q = charge on the capacitor #44 Speed of a Wave on a String C = capacitance of the capacitor mv 2 V = voltage applied to the capacitor T= RC Circuits (Discharging) L - t/RC Vc = Voe T = tension in string Vc - IR = 0 m = mass of string L = length of string #60 Thermal Expansion #45 Projectile Motion Linear: L = LoT Horizontal: x-x= vt + 0 Vertical: y-y = vt + at Volume: V = VoT #46 Centripetal Force #61 Bernoulli's Equation mv 2 P + gh + v = constant F= = m 2 r QVolume Flow Rate = A1v1 = A2v2 = constant r #62 Rotational Kinetic Energy (See LEM, pg 8) #47 Kirchhoff's Laws 2 KErotational = I = I (v / r)2 Loop Rule: Around any loop Vi = 0 2 KErolling w/o slipping = mv2 + I Node Rule: at any node Ii = 0 #51 Minimum Speed at the top of a Angular Momentum = L = I = mvrsin Vertical Circular Loop Angular Impulse equals CHANGE IN Angular Momentum v = rg L = orquet = (I) Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 3 of 8 #75 Thin Lens Equation #63 Period of Simple Harmonic Motion f = focal length T = 2 m where k = spring constant 1 1 1 1 1 i = image distance = + = + k f D o D i o i o = object distance f = 1 / T = 1 / period #64 Banked Circular Tracks Magnification v2 = rgtan M = - D i / Do = - i / o = H i / Ho #66 First Law of Thermodynamics Helpful reminders for mirrors and lenses U = QNet + WNet Focal Length of: positive negative Change in Internal Energy of a system = mirror concave convex +Net Heat added to the system lens converging diverging +Net Work done on the system Object distance = o all objects Object height = Ho all objects Flow of Heat through a Solid Image distance = i real virtual Q / t = kAT / L Image height = Hi virtual, upright real, inverted k = thermal conductivity Magnification virtual, upright real, inverted A = area of solid L = thickness of solid #76 Coulomb's Law q1 q 2 #68 Potential Energy stored in a Capacitor F =k P = CV r2 1 N m2 k= = 9E9 RC Circuit formula (Charging) 4 o C2 - t / RC Vc = Vcell(1 - e ) #77 Capacitor Combinations RC = = time constant PARALLEL Vcell - Vcapacitor - IR = 0 Ceq = C1 + C2+ C3 + ... SERIES n 1 1 1 1 1 #71 Simple Pendulum C eq = + C1 C 2 +K + Cn = Ci =1 i L and f = 1/ T T = 2 g #78 Work done on a gas or by a gas W = PV #72 Sinusoidal motion x = Acos(t) = Acos(2f t) #80 Electric Field around a point charge = angular frequency q E=k f = frequency r2 #73 Doppler Effect 1 N m2 k = = 9E9 343 Toward vo 4 o C2 f= f Away 343 m Toward Away vs #82 Magnetic Field around a wire vo = velocity of observer: vs = velocity of source I B= o 2 r #74 2nd Law of Thermodynamics Magnetic Flux The change in internal energy of a system is = BAcos U = QAdded + WDone On Qlost WDone By Force caused by a magnetic field Maximum Efficiency of a Heat Engine on a moving charge (Carnot Cycle) (Temperatures in Kelvin) F = qvBsin Tc % Eff = (1 - ) 100% #83 Entropy change at constant T Th S = Q / T (Phase changes only: melting, boiling, freezing, etc) Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 4 of 8 #95 Relativistic Time Dilation #84 Capacitance of a Capacitor t = to / C = oA / d = dielectric constant #96 Relativistic Length Contraction A = area of plates x = xo d = distance between plates o = 8.85 E(-12) F/m Relativistic Mass Increase m = mo / #85 Induced Voltage N = # of loops #97 Energy of a Photon or a Particle Emf = N E = hf = mc2 t Lenz's Law induced current flows to create a B-field h = Planck's constant = 6.63 E(-34) J sec opposing the change in magnetic flux. f = frequency of the photon #86 Inductors during an increase in current #98 Radioactive Decay Rate Law -kt VL = Vcelle - t / (L / R) A = Aoe = (1/2n)A0 (after n half-lives) Where k = (ln 2) / half-life - t / (L / R) I = (Vcell/R)[ 1 - e ] #99 Blackbody Radiation and L / R = = time constant the Photoelectric Effect #88 Transformers E= nhf where h = Planck's constant N 1 / N 2 = V 1 / V2 I1V1 = I2V2 #100 Early Quantum Physics #89 Decibel Scale Rutherford-Bohr Hydrogen-like Atoms B (Decibel level of sound) = 10 log ( I / Io ) I = intensity of sound 1 1 1 Io = intensity of softest audible sound = R - 2 meters -1 2 ns n or #92 Poiseuille's Law P = 8LQ/(r ) 4 c 1 1 f = = cR - 2 Hz = coefficient of viscosity 2 ns n L = length of pipe R = Rydberg's Constant r = radius of pipe = 1.097373143 E7 m-1 Q = flow rate of fluid ns = series integer (2 = Balmer) Stress and Strain n = an integer > ns Y or S or B = stress / strain stress = F/A Mass-Energy Equivalence Three kinds of strain: unit-less ratios mv = mo / I. Linear: strain = L / L Total Energy = KE + moc2 = moc2 / II. Shear: strain = x / L Usually written simply as E = m c2 III. Volume: strain = V / V de Broglie Matter Waves #93 Postulates of Special Relativity For light: Ep = hf = hc / = pc 1. Absolute, uniform motion cannot be detected. Therefore, momentum: p = h / 2. No energy or mass transfer can occur Similarly for particles, p = mv = h / , at speeds faster than the speed of light. so the matter wave's wavelength must be =h/mv #94 Lorentz Transformation Factor Energy Released by Nuclear v2 Fission or Fusion Reaction = 1- 2 E = moc2 c Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 5 of 8 MISCELLANEOUS FORMULAS Fundamental SI Units Unit Base Unit Symbol Quadratic Formula ......................... if a x + b x + c = 0 Length meter m then Mass kilogram kg - b b - 4ac 2 Time second s x= 2a Electric Current ampere A Trigonometric Definitions Thermodynamic sin = opposite / hypotenuse Temperature kelvin K cos = adjacent / hypotenuse Luminous tan = opposite / adjacent Intensity candela cd Quantity of sec = 1 / cos = hyp / adj Substance moles mol csc = 1 / sin = hyp / opp cot = 1 / tan = adj / opp Plane Angle radian rad Inverse Trigonometric Definitions Solid Angle steradian sr or str = sin-1 (opp / hyp) = cos-1 (adj / hyp) = tan-1 (opp / adj) Some Derived SI Units Symbol/Unit Quantity Base Units Law of Sines ......................... a / sin A = b / sin B = c / sin C C coulomb Electric Charge As or sin A / a = sin B / b = sin C / c F farad Capacitance A2s4/(kgm2) Law of Cosines H henry Inductance kgm2/(A2s2) a = b + c2 - 2 b c cos A 2 2 b2 = c2 + a2 - 2 c a cos B Hz hertz Frequency s-1 c = a + b - 2 a b cos C J joule Energy & Work kgm2/s2 = Nm T-Pots For the functional form N newton Force kgm/s2 1 1 1 = + ohm Elec Resistance kgm2/(A2s2) A B C Pa pascal Pressure kg/(ms2) You may use "The Product over the Sum" rule. B C T tesla Magnetic Field kg/(As2) A= B+C V volt Elec Potential kgm2/(As3) For the Alternate Functional form 1 1 1 W watt Power kgm2/s3 = - A B C Non-SI Units o C degrees Celsius Temperature You may substitute T-Pot-d B C B C eV electron-volt Energy, Work A= =- C-B B-C Version 5/12/2005Download Link: