`Algebra and Trigonometry based Physics Formula sheetShadow J.Q. Robinson11Department of Physics, Millsaps College, Jackson, MS 39210 [email protected]The presence of a formula does not guarantee its use! Students are always welcome to suggest changes additions deletions corrections etc.I.UNIT PREFIXESGiga (G)- 1 billion or 109 Mega (M)- 1 million or 106 kilo (k)- 1 thousand or 103 centi (c) - 1 hundredth or 10-2 milli (m) - 1 thousandth or 10-3 micro (µ) - 1 millionth or 10-6 nano (n) - 1 billionth or 10-9where v is speed of particle and r is radius of the circular arc traveled by the particle. Centripetal Force = mass x centripetal acceleration. Newton's Law of Gravitation F =G M1 M2 R2 (11)where G = 6.67 x 10-11 N m2 / kg2 , the M's are the masses of the two bodies and R is the distance between their centers. For a constant force, work is given by W = F dcos (12)II.EQUATIONS FOR PHYSICS EXAMAlways x - x0 = vavg t For constant acceleration v = v0 + at 1 (x - x0 ) = v0 t + at2 2 2 v 2 = v0 + 2a(x - x0 ) v + v0 vavg = 2 Acceleration from free fall a = -g = -9.8 m s2 (6) (2) (3) (4) (5) (1)where F is the constant force, d is the displacement and  is the angle between the F and d vectors. Work Energy Principle Wnet = KE 1 where KE = Kinetic Energy = mv 2 2 Force from spring F = -kx (14) (13)where x is the displacement from equilibrium and k is the spring constant. Potential energies for conservative forces P Egrav = mgy 1 P Espring = kx2 2 Work by a conservative force (15) (16)III.DYNAMICSNewton's Second Law Fnet = ma Force of kinetic friction (7)Wcons = -P E If only conservative forces, KE + P E = 0(17)(18)Ff r = µk N where N is the normal force. Force of static friction Ff r  µs N(8) Momentum p = mv (9) Newton's second Law in terms of momentum F = p t (20) (19)where N is the normal force. Centripetal acceleration, points inward (along radius of circle) v2 aR = r (10)For elastic head on collisions v1 - v2 = -(v1f - v2f ) (21)2 For constant angular acceleration  = 0 + t 1  = 0 t + t2 2 2  2 = 0 + 2  + 0 avg = 2 Relation to linear motion l = r v = r atan = r acentripetal = r 2 Torque  = F rsin  = I Moment of Inertia2 I = mi riBernoulli Equation (22) (23) (24) (25) Period of spring (26) (27) (28) (29) T = 2 Period of Pendulum T = 2 (30) (31) Wave velocity v = f (32) Wave Intensity I= P 4r2 (47) (46) L g (45) m k (44) f= 1 T (43) 1 1 P1 + 1 v 2 + gh1 = P2 + 2 v 2 + gh2 2 2 Frequency and Period (42)Rotational Kinetic energy KErot = Angular momentum L = I Newton's second law  = Conditions for equilibriumIV.1 2 I 2(33)Sound Intensity  = 10log I I0 (48)(34)where I0 = 10-12 W/m2 . Doppler Effect f =f v ± vobs v ± vsource (49)L t(35)ELECTRIC FORCE AND FIELDSF = 0  = 0 Density m = V Pressure P = F A(36) (37)Force between two point charges q1 and q2 Felectric = kq1 q2 r2 (50)(38)(39)where direction is given by repulsion or attraction of the charges. I am fine if you use the approximation of k=9x109 N m2 /C 2 Electric field of a point charge q E= kq r2 (51)Pressure at depth h in fluid P = gh Atmospheric Pressure Patm = 1.103x105 Pascal Equation of continuity A1 1 v1 = A2 2 v2 (41) (40)Electric fields relation to Electric force E= F q (52)Electric Potential at any point in space defined as electric potential energy per unit charge3Va =P Ea q(53)V = V0 sin(t) I = I0 sin(t) Root mean square values(64) (65)P E = qV(54)Inside a uniform electric field, the change in potential is given by Vba = -Ed (55)I0 Irms =  2 V0 Vrms =  2 Power in AC circuit P = Irms Vrms Adding resistors in series Ref f = R1 + R2 + R3 Adding resistors in parallel 1 Ref f = 1 1 1 + + R1 R2 R3(66) (67)where E is the electric field and d is the distance traveled in the uniform field. For a point charge V = Capacitance C = Q/V For Parallel Plates A d (57) kq r (56)(68)(69)(70)Kirchoff's rules 1. Current into a junction = current out of a junction. 2. Total change in potential around closed loop = 0. SI Units for magnetic field Tesla , also sometimes see Gauss where 104 Gauss = 1 Tesla Force on electric current in a magnetic field F = IlBsin Force on moving charge in a magnetic field, F = qvBsin Magnetic field from a long straight wire (72) (71)C=0(58)1 Where 0 is given by the relation k= 4 In the presence of a dielectric with a dielectric constant , the value of 0 is replaced by  0 Energy stored in a capacitor PE = Ohm's Law V = IR (60) 1 1Q 1 QV = CV 2 = 2 2 2 C2(59)B=µ0 I 2r B t(73)V is potential difference in Volts, I is current in Amps, and R is resistance in Ohms which is denoted by . For a material, R= L A (61)Induced electro-motive force  = -N Transformer equation VS NS = VP NP velocity of light = c (74)where  is the resistivity and L is the length of wire and A is the cross sectional area. Temperature dependence T = 0 (1 + (T - T0 )) Power P = IV = I 2 R = V 2 /R AC Current Law of Reflection: (63) (62)(75)c = f = 3x108 m/s(76)i = r(77)4 Snell's Law or Law of Refraction n1 sin1 = n2 sin2 For mirrors and thin lenses: Microscope 1 1 1 + = do di f Magnification m= focal length for mirror f = R/2 (81) = -di do (80) is approximately fNflo . e Special Relativity Relativistic factor 1 1 - v 2 /c2 (89) (79) M= N l - fe fe d0 (78) M = -f0 /fe (87) for eye focused at the near point Telescope(88)Interference: Light interference gives a maxima when the waves have a total difference of an integer number of wavelength. It is a minimum when the waves have a half-integer difference. Wavelength in medium: 0 nt = t0(90)L= (82)L0 (91)n =m = m0(92)where 0 is the wavelength in a vacuum. Double Slit: Path difference = d sin  where d is the separation of the slits and theta is the angle to the screen position measured from between the slits. For constructive dsin = n For destructive dsin = (n + 1/2) (84) (83)Where the quantities with subscript 0 are the values recorded in the rest frame of the object, and the one without is the value measured by an observer seeing the object move at speed v and c is the speed of light. deBroglie wavelength h p=(93)where h is Planck's constant and p is momentum.Single slit: Diffraction minima are located at d sin  = n  where n is an integer. Reflection on thin films, if the light in a lower index of refraction bounces off of a higher n material, a phase change of 1/2  occurs. If light in a higher n material bounces off a lower n material, no change occurs. Magnifying glass M = N/f (85)V.ALGEBRA AND TRIGONOMETRYsin2  + cos2  = 1 sin2 = 2sincos Quadratic formula ax2 + bx + c = 0 is solved by x= -b ±  b2 - 4ac 2a(94) (95)(96)for relaxed eye, N=near point of the eye, for adults approx 25 cm. M = N/f + 1 (86)(97)`

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