33471063 SC Physics Formulas

PhysicsForm 8.0 4/15/03 12:16 PM Page 1 PHYSICAL CONSTANTS ELECTROMAGNETIC CONSTANTS Acceleration due to gravity g 9.8 m/s 2 WAVELENGTHS OF LIGHT IN A VACUUM (m) Avogadro’s number NA 6.022 × 10 23 molecules /mol Red 6.5 – 7.0 × 10−7 ƒ = frequency (in Hz) Orange 5.9 – 6.5 × 10−7 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 Coulomb’s constant k 9 × 109 N·m2 /C2 radio gamma Yellow 5.7 – 5.9 × 10−7 waves microwaves infrared ultraviolet X rays rays Gravitational constant G 6.67 × 10−11 N·m2 /kg 2 Green 4.9 – 5.7 × 10−7 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 = wavelength (in m) R O Y G B I V Planck’s constant h 6.63 × 10 −34 J·s Blue 4.2 – 4.9 × 10−7 = 780 nm visible light 360 nm Violet 4.0 – 4.2 × 10−7 Ideal gas constant R 8.314 J/(mol·K) = 0.082 atm ·L/(mol·K) INDICES OF REFRACTION FOR COMMON SUBSTANCES ( l = 5.9 X 10 –7 m) Permittivity of free space ε0 8.8541 × 10−12 C/(V·m) Air 1.00 Alcohol 1.36 Corn oil 1.47 Diamond 2.42 Permeability of free space µ0 4π × 10−7 Wb/(A·m) Glycerol 1.47 Water 1.33 Speed of sound at STP 331 m/s Speed of light in a vacuum c 3.00 × 108 m/s OPTICS REFLECTION AND REFRACTION incident ray Electron charge e 1.60 × 10 −19 C Law of Reflection θinciden t = θreflected angle of Electron volt eV 1.6022 × 10 −19 J c incidence 01 normal Index of refraction n= (v is the speed of light in the medium) angle of 0' 02 angle of v refraction Atomic mass unit u 1.6606 × 10 kg −27 reflection Snell’s Law n1 sin θ1 = n2 sin θ2 refracted ray = 931.5 MeV/c2 � � reflected ray Rest mass of electron me 9.11 × 10−31 kg Critical angle θc = sin −1 nn21 = 0.000549 u = 0.511 MeV/c2 LENSES AND CURVED MIRRORS 1 1 1 image size q ...of proton mp 1.6726 × 10−27 kg + = =− p q f object size p = 1.00728 u = 938.3 MeV/c2 Optical instrument Focal distance f Image distance q Type of image Lens: …of neutron 1.6750 × 10−27 kg Concave negative negative (same side) virtual, erect 1 = 1.008665 u p = 939.6 MeV/c2 Convex positive p<f negative (same side) virtual, erect 2 p>f positive (opposite side) real, inverted 3 h V Mass of Earth 5.976 × 1024 kg Mirror: F Radius of Earth 6.378 × 10 m 6 Convex negative negative (opposite side) virtual, erect 4 q Concave positive p<f negative (opposite side) virtual, erect 5 positive (same side) real, inverted 6 6 DYNAMICS p>f NEWTON’S LAWS 1. First Law: An object remains in its state of rest or motion with h h h F q h h F V V V V F V F constant velocity unless acted upon by a net external force. F F F p p p p q p q dp q 2. Second Law: Fnet = ma F = q 2 4 dt 1 3 5 3. Third Law: For every action there is an equal and opposite reaction. Weight Fw = mg WORK, ENERGY, POWER KINEMATICS Work W = F · s = F s cos θ Normal force FN = mg cos θ (θ is the angle to the horizontal) � Average DISTANCE W = F · ds ∆s velocity vavg = s (m) FRICTION ∆t 1 p2 Static friction fs, max = µs FN Kinetic friction fk = µk FN Kinetic energy KE = mv 2 = 2 2m µs is the coefficient of static friction. Instantaneous ds Work-Energy Theorem W = ∆KE velocity v= µk is the coefficient of kinetic friction. (for conservative forces) dt For a pair of materials, µk < µs . ∆U = −W � Potential energy Displacement ∆s = v dt t (s) UNIFORM CIRCULAR MOTION Gravitational $5.95 CAN v2 mv 2 potential energy Ug = mgh Average VELOCITY Centripetal acceleration ac = Centripetal force Fc = ∆v r r acceleration aavg = v (m/s) Total mechanical ∆t energy E = KE + U + Instantaneous VECTOR FORMULAS ∆W acceleration a= dv $3.95 Average power Pavg = dt ∆t Notation a = ax î + ay î + az k̂ t (s) Instantaneous Change � in velocity ∆v = a dt � Magnitude a = |a| = a2x + a2y + a2z power P =F·v CONSTANT – Dot product a · b = ax bx + ay by + az yz MOMENTUM AND IMPULSE (θ is the angle between a and b) = ab cos θ ACCELERATION Linear momentum p = mv vf = v0 + at ACCELERATION Cross product |a × b| = ab sin θ Impulse J = �Ft = ∆p 1 a (m/s2) axb vavg = (v0 + vf ) a × b points in the a J= F dt = ∆p 2 + direction given by a 1 the right-hand rule: COLLISIONS s = s0 + v0 t + at 2 b b All collisions m1 v1 + m2 v2 = m1 v1� + m2 v2� 1 t (s) = s0 − vf t + at a × b = (ay bz − az by ) î + (az bx − ax bz) ĵ + (ax by − ay bx ) k̂ Elastic collisions 2 1 1 1 1 � � � ax ay az �� = �� ax � ay bz �� 2 2 2 2 m1 v12 + m2 v22 = m1 (v1� ) + m2 (v2� ) 2 2 = s0 + vavg t – � î ĵ k̂ � v1 − v2 = − (v1� − v2� ) vf2 = v02 + 2a(sf − s0 ) CONTINUED ON OTHER SIDE This downloadable PDF copyright © 2004 by SparkNotes LLC. SPARKCHARTS™ Physics Formulas page 1 of 2 1. T = 2π � ∆ω dω g Biort-Savart Law dB = αavg = α= 4π r2 ∆t dt mg sin 0 Design: Dan O. Escape velocity vescap e = r ∆Qout Rotational KE rot = 12 Iω 2 Alternatively. PhysicsForm 8. λeff = λ � feff = f v±v o v±vs feff = f v−v � MAGNETISM o v Magnetic force on moving charge F = qvB sin θ F = q (v × B) ROTATIONAL SIMPLE HARMONIC Magnetic force on current-carrying wire F = BI� sin θ F = I (� × B) MOTION MOTION s MAGNETIC FIELD PRODUCED BY… Angular position θ= PENDULUM µ0 qv × r̂ r Magnetic field due to a moving charge B= Velocity at equilibrium 4π r2 v Angular velocity ω= position r µ0 I v= 2g� (1 − cos θmax ) Magnetic field produced by a current-carrying wire B= � Series Editors: Sarah Friedberg. Justin Kestler ∆θ dθ 2π r ωavg = ω= Illustration: Dan O.0 4/15/03 12:16 PM Page 2 WAVES ELECTRICITY Amplitude A Frequency f Wavelength λ Period T Angular frequency ω ELECTROSTATICS q1 q2 1 q1 q2 1 2π 2π Coulomb’s Law F =k = T = = ω = 2πf = r2 4πε0 r 2 f ω T Wave speed v = f λ Fon q Electric field E= F = Eq q Wave equation W y(x. SPARKCHARTS™ Physics Formulas page 2 of 2 . .95 CAN 1 dt ωf = ω0 + αt ωavg = (ω0 + ωf ) v=0 v = max v=0 2 U = max U = min U = max MAXWELL’S EQUATIONS KE = 0 KE = max KE = 0 1 θ = θ0 + ω 0 t + Qenclosed � αt equilibrium 2 Gauss’s Law E · dA = $3. Downer. Motion of source Veq = V1 + V2 + V3 + · · · Motion of observer Stationary Toward observer Away from observer at vs at vs Req = R1 + R2 + R3 + · · · Stationary v veff = v veff = v Parallel circuits R1 λeff = λ v−v λeff = λ v+v � � � � λ s s Ieq = I1 + I2 + I3 + · · · R2 � v � � v � f feff = f v−v v feff = f v+v v Veq = V1 = V2 = V3 = . The imaginary segment connecting the planet to the Sun sweeps out equal areas in equal time. Report errors at � Moment of inertia I= r 2 dm � and k is the spring constant. GM Earth Torque τ = F r sin θ Acceleration due to gravity a= 2 dL τ =r×F THERMODYNAMICS rEarth τ = dt τ = Iα 1. Planets revolve around the Sun in an elliptical path with the Sun at one focus. . the efficiency e = 1 − ∆Qin KEPLER’S LAWS OF PLANETARY MOTION kinetic energy of any heat engine always satisfies 0 ≤ e < 1.95 position ε0 = θ0 + ωavg t �s MASS-SPRING SYSTEM Gauss’s Law for magnetic fields B · dA = 0 4 ωf2 = ω02 + 2α(θf − θ0 ) Restoring force F = −k(∆)x �s www. t) = A sin(kx − ωt) = A sin 2π λx − t � � �� T Potential difference ∆V = q TM SPARKCHARTS WAVE ON STRING CIRCUITS mass Tension in string FT Length L Mass density µ = ∆Q length Current I= � ∆t FT L Speed of standing wave v= Resistance R=ρ µ A 2L V Wavelength of standing wave λn = Ohm’s Law I= n R SOUND WAVES Power dissipated by resistor P = V I = I 2R Beat frequency fbeat = |f1 − f2 | Heat energy dissipated by resistor W = P t = I 2 Rt DOPPLER EFFECT Series circuits R1 R2 R3 Ieq = I1 = I2 = I3 = . Williams. T1 T2 T1 T2 a3 This downloadable PDF copyright © 2004 by SparkNotes LLC. Ampere’s Law B · ds = µ0 Ienclosed 1 �c particle sphere Elastic potential energy Ue = k(∆x)2 ∂ � 1 1 2 Ampere-Maxwell Law B · ds = µ0 Ienclosed + µ0 ε0 E · dA MR 2 MR 2 ML2 R 2 R 12 � m c ∂t s R R Period T = 2π k GRAVITY 2 MR 2 MR 2 L 5 ring disk rod Equation of motion x = A sin(ωt) m1 m2 7 � TORQUE AND ANGULAR where ω = 2π T = k m is the angular frequency Newton’s Law of Universal Gravitation F =G r2 MOMENTUM and A = (∆x)max is the amplitude. Universal Gas Law P V = nRT Boyle’s Law P1 V1 = P2 V2 3. R3 s s 1 1 1 1 = + + + ··· Towards source at vo veff = v + vo Req R1 R2 R2 λeff = λ � veff = v ± vo KIRCHHOFF’S RULES feff = f v+v o � λeff = λ v±v v � s � Loop rule: The sum of all the (signed) potential differences around any closed loop is zero. The square of the period of revolution is directly proportional to the cube of the length of P1 V1 P2 V2 P1 P2 the semimajor axis of revolution: T 2 Combined Gas Law = Charles’s Law = is constant. . Second Law: All systems tend � GM L=r×p L = Iω spontaneously toward maximum entropy. Williams CONSTANT a mg mg cos 0 Lenz’s Law and Faraday’s Law ε=− dΦB $5.com/errors ∂ΦB ∂ � ∆x is the distance the spring is stretched or E · ds = − =− B · dA 20593 36340 MOMENTS OF INERTIA (I ) Faraday’s Law c ∂t ∂t s compressed from the equilibrium position. .sparknotes. v Away from source at vo veff = v − vo � � Node rule: The total current entering a juncture must equal the total current leaving the juncture. GAS LAWS 2. Matt Daniels ∆t dt 0 Magnetic field produced by a solenoid B = µ0 nI at Period Angular acceleration α= T Anna Medvedovsky r � µ0 I (d� × r̂) Contributors: Bernell K. First Law GM m Gravitational potential U (r) = − ∆ (Internal Energy) = ∆Q + ∆W r Angular momentum L = pr sin θ 2.