| 14374078844 | Dot Product A*B= | |A||B|cos theta | | 0 |
| 14374078845 | Cross Product AxB= | |A||B|sin theta | | 1 |
| 14374078846 | Gravitational Force Fg= | Gm1m2 / r^2; G= 6.67x 10^-11 N*m^2/kg^2 | | 2 |
| 14374078847 | Kinetic friction | fk= (mu)k * Normal Force (N) | | 3 |
| 14374078848 | Relationship between static and kinetic friction | 0<=fs <= (mu)s * Normal force | | 4 |
| 14374078849 | Center of gravity | x=(m1*x1 + m2*x2 + ....+ mnxn)/(m1 + m2 +....+ mn); Do the same for y and z | | 5 |
| 14374078850 | Average Acceleration | a= deltav/deltat | | 6 |
| 14374078851 | Instantaneous acceleration | a= lim (deltav/deltat) as t->0; a= dv/dt | | 7 |
| 14374078852 | Kinematics with vf, vi, a, and t | Vf=Vi + a* t -> (m/s) = (m/s) + (m/s^2)*(s) | | 8 |
| 14374078853 | Kinematics with x, Vi, t, and a | X= Vi*t + (1/2)*a*t^2 -> (m)= (m/s)*(s) + (1/2)*(m/s^2)*(t^2) | | 9 |
| 14374078854 | Kinematics with Vf, Vi, a, and X | Vf^2 = Vi^2 + 2*a*x -> (m^2/s^2) = (m^2/s^2) + 2*(m/s^2)*(m) | | 10 |
| 14374078855 | Kinematics with X, V, and t | X= Vt -> (m) = (m/s)*(t) | | 11 |
| 14374078856 | Centripital Force | Fc = (mv^2)/r = m * centripital acceleration = m * v^2/r | | 12 |
| 14374078857 | Centripital acceleration | v^2/r | | 13 |
| 14374078858 | Period of circular motion | T= (2*pi*r)/v -> v= (circumference)/time | | 14 |
| 14374078859 | Angular Speed of circular motion | w= (2*pi)/ T -> w= v/r by substituting T. Makes sense as 2pi radians is a full circle | | 15 |
| 14374078860 | torque | torque = r x F = rFsintheta | | 16 |
| 14374078861 | Kinetic Energy | KE= (1/2)*m*v^2 | | 17 |
| 14374078862 | Gravitational potential energy | U = m*g*h | | 18 |
| 14374078863 | Elastic Potential Energy | U = (1/2)*k*x^2; where k is the spring constant and x is the magnitude of displacement | | 19 |
| 14374078864 | Work done by nonconservative forces | Wnonconservative = Delta E = DeltaU + DeltaK; Where U is potential energy and K is kinetic energy | | 20 |
| 14374078865 | Work Formula | Force * Distance = Fdcostheta; Unit is Joule = (kg*m^2)/s^2) | | 21 |
| 14374078866 | Power Formula | P = W/t = DeltaE/t; Amount of work done per unit time; | | 22 |
| 14374078867 | Net Work formula | Wnet = DeltaK = Kf - Ki | | 23 |
| 14374078868 | Mechanical Advantage | Fout/Fin | | 24 |
| 14374078869 | Efficiency | Wout/Win = load * load distance / effort * effort distance; load distance may not equal effor distance | | 25 |
| 14374078870 | Work in isobaric system | W= P* DeltaV; Using P= F/A this makes sense. Units being N*m | | 26 |
| 14374078871 | Work from a P-V Graph | Work = area under curve | | 27 |
| 14374078872 | Farenheit and Celsius Conversion | F=(9/5)C+32 | | 28 |
| 14374078873 | Celsius and Kelvin Conversion | K = C + 273 | | 29 |
| 14374078874 | Linear Expansion Equation | DeltaL = alpha*L*DeltaT; alpha is the coefficient of linear expansion | | 30 |
| 14374078875 | Volumetric Expansion Equation | DeltaV = Beta*V*Delta T | | 31 |
| 14374078876 | Coefficient of volumetric expansion (Beta) from coefficient of linear expansion (alpha) | Beta = 3* Alpha | | 32 |
| 14374078877 | Change in Systems internal Energy Equation | Delta U = Q - W; Q is energy transferred into the system as heat, W is the work done by the system | | 33 |
| 14374078878 | Heat Transfer Equation and what its used for | q = m*c*DeltaT; where c is the specific heat; mass is grams; Used for calorimetry | | 34 |
| 14374078879 | Formula for Heat of Transformation | q = m*L; where L is the heat of transformation or latent heat, usually given | | 35 |
| 14374078880 | Change in Entropy Equation | DeltaS = Q(rev)/T; where Q is the heat gained or lost in a reversible reaction | | 36 |
| 14374078881 | Specific Gravity | Density substance / Density of water; Density of water = 1g/cm^3 or 1000 kg/m^3 | | 37 |
| 14374078882 | Absolute (Hydrostatic) Pressure | P = Po + density*g*depth; Check units. P= F/A (N/m^2); where Po is the pressure at surface | | 38 |
| 14374078883 | Pgauge formula | Pgauge = Pabs - Patm; i.e. the difference in pressure between surface and object | | 39 |
| 14374078884 | Bouyant Force | Fb= density(fluid)*V(fluid displaced)*g = density(fluid)*V(submerged)*g | | 40 |
| 14374078885 | Ratio of object submerged | Ratio = density of object/ density of fluid; Can be derived from sum of forces on floating object | | 41 |
| 14374078886 | Rate of laminar flow | Q=(pi*r^4*DeltaP)/(8*n*L); where n is the viscosity | | 42 |
| 14374078887 | Critical speed of fluid flow | Vc = (Nr*n)/(density*D); where Nr is Reynold's number and is usually given; at this speed we go from laminar to turbulent flow | | 43 |
| 14374078888 | Flow rate with respect to linear speed and area | Q (flow rate) = V1A1 = V2A2; units work out such that it's m^3/s | | 44 |
| 14374078889 | Bernoulli's Equation | Static Pressure 1 + Dynamic Pressure 1 = Static Pressure 2 + Dynamic Pressure 2; P +density*g*h + (1/2)*density*V^2 = Same thing on other side | | 45 |
| 14374078890 | Force on a charge | Fe = (kQq)/r^2; where k is coulomb's constant (aka electrostatic constant) OR Fe = qE | | 46 |
| 14374078891 | Magnitude of an electric field | E = (Fe/q) = Force felt by test charge / test charge Or E = (kQ)/r^2 where Q is the source charge | | 47 |
| 14374078892 | Electric Potential Energy | U = (kQq)/r; Makes sense as Delta U=W = Fdcostheta = F*d = [(kQq)/r^2]*r | | 48 |
| 14374078893 | Electric Potential Equation | V= kQ/r | | 49 |
| 14374078894 | Work done by moving a charge across an electric field | Wab = qDeltaV | | 50 |
| 14374078895 | Dipole Moment | p = q*d | | 51 |
| 14374078896 | Torque of a dipole in electric field | T1=F*r*sintheta -> T1=qE*r*sin(theta) -> Total torque = 2*qE*r*sin(theta) = qE * d * sin(theta) = pEsin(theta) | | 52 |
| 14374078897 | Potential energy of Dipole in electric field | ***U = -p*E*cos(theta)*** Zero at 90 degrees because at 180 degrees it is at maximum and at 0 degrees it is at minimum | | 53 |
| 14374078898 | Magnetic Field for straight wire @ any distance r from the wire | B = (mu*I)/(2*pi*r) | | 54 |
| 14374078899 | Magnetic Field for a circular loop @ center of loop | B = (mu*I)/(2*r) | | 55 |
| 14374078900 | Magnetic force on charge in field | F = qvBsin(theta) | | 56 |
| 14374078901 | Current | I = Q/Deltat | | 57 |
| 14374078902 | Resistance | R = (resistivity (rho) * L) / A | | 58 |
| 14374078903 | Ohm's Law | V = IR | | 59 |
| 14374078904 | True voltage of a circuit | V = Ecell - i*r(int); where Ecell is emf, r(int) is the internal resistance | | 60 |
| 14374078905 | Power in circuit | P = IV = I^2*R = V^2 / R | | 61 |
| 14374078906 | Resistors in series | Add | | 62 |
| 14374078907 | Resistors in parallel | Add inversely | | 63 |
| 14374078908 | Capacitors in series | Add inversely | | 64 |
| 14374078909 | Capacitors in parallel | Add | | 65 |
| 14374078910 | Capacitance of a parallel plate capacitor | C = Eo*(A/d); where Eo is the permittivity of free space = 8.85 x 10^ -12 (F/m) | | 66 |
| 14374078911 | Uniform electric field across a parallel plate capacitor | E = V/d | | 67 |
| 14374078912 | Voltage across an electric field | V = E x r -> V=E*d for a parallel plate capacitor | | 68 |
| 14374078913 | Potential energy of a capacitor | U = (1/2)*C*V^2 | | 69 |
| 14374078914 | Capacitance of a capacitor with a dielectric material | C' = kC -> C=k * (Eo) * (A/d) -> C = (A*k*Eo) / d | | 70 |
| 14374078915 | propagation speed of a wave | v = f*lambda | | 71 |
| 14374078916 | Period of a wave | T = 1 / f | | 72 |
| 14374078917 | Angular frequency (w) | w = 2*pi*f = (2*pi) / T | | 73 |
| 14374078918 | Speed of Sound | Sqrt(B/density); where B is the 'bulk modulus' and density is that of the medium | | 74 |
| 14374078919 | Doppler Equation | f ' = f [ (V +- Vd) / (V -+Vs) ]; Use 'left' if detector or source is moving toward the other. Use 'right' if detector or source is moving away from the other | | 75 |
| 14374078920 | Sound intensity | P/A where A is surface area | | 76 |
| 14374078921 | Surface area of a sphere | A = 4*pi*r^2 | | 77 |
| 14374078922 | Sound Level Formula | B = 10 log (I / Io); where B is measured in dB, I is intensity of the sound wave and Io is the threshold of hearing (1x10^-12 W/m^2) | | 78 |
| 14374078923 | Altered Sound Level Formula | Bf = Bi + 10 log (If / Ii); Can be derived from Sound Level Formula (DeltaB) | | 79 |
| 14374078924 | Given string fixed at two ends: What are the lengths that correspond to each harmonic? (1st, 2nd, and 3rd) | They are L = (1/2)lambda, lambda, (3/2)lambda; We can draw them. # of ANTINODES = Harmonic #. Use equation L=(A.N./2)*lambda where A.N is # of Antinodes | | 80 |
| 14374078925 | Given a pipe open on both ends: What are the lengths that correspond to each harmonic? (1st, 2nd, and 3rd) | They are L = (1/2)lambda, lambda, (3/2)lambda; We can draw them. # of NODES = Harmonic #. Use equation L=(N/2)*lambda where N is # of Nodes | | 81 |
| 14374078926 | For a string fixed on both ends and an open pipe (one that's open on both ends), What are the frequencies for each harmonic | f = (n*v) / (2*L) where n is the harmonic #; i.e. number of A.N. in fixed string, and number of N for open pipe | | 82 |
| 14374078927 | For a closed pipe (One that is closed on one end), what are the lengths that correspond to each harmonic? | The only harmonics of a closed pipe are odd harmonics. Use formula L= lambda * [(N + A.N.-1) / 4]; Numerator corresponds to the harmonic | | 83 |
| 14374078928 | For a closed pipe (One that is closed on one end), what are the frequencies that correspond to each harmonic? | f = (n*v) / (4*L) where n is the harmonic # -> Harmonic # = ( N + A.N. -1) | | 84 |
| 14374078929 | Speed of light formula | c=f*lambda | | 85 |
| 14374078930 | Law of reflection | Theta1 = Theta2; Theta is with respect to the normal vector | | 86 |
| 14374078931 | Focal length | Distance from mirror to Focal Point (F); f = r/2; where r is the radius of curvature | | 87 |
| 14374078932 | Distance between Object (O) and mirror is | 'o' | | 88 |
| 14374078933 | Distance between Image (I) and mirror is | 'i' | | 89 |
| 14374078934 | Distance between Center of Curvature (C) and mirror | 'r' | | 90 |
| 14374078935 | Distance between Focal Point (F) and mirror | 'f' | | 91 |
| 14374078936 | Equation for mirrors and lenses | (1/f) = (1/'o') + (1/i) = (2/'r') | | 92 |
| 14374078937 | If i is positive | The image is real - image is on "same side as you" | | 93 |
| 14374078938 | If i is negative | The image is virtual - image is "on the side opposite of you" | | 94 |
| 14374078939 | If o is positive | Object is in front/on the light source side | | 95 |
| 14374078940 | If o is negative | Object is behind/on the opposite side of light source | | 96 |
| 14374078941 | Equation for plane mirror | i = -o; Plane mirrors essentially have an r that is infinity | | 97 |
| 14374078942 | Equation for magnification | m = -i / o; If |m|<1 then the image is smaller than object. If |m|>1, then image is magnified; m<0 then inverted; m>0, upright. | | 98 |
| 14374078943 | Positive r is always | converging | | 99 |
| 14374078944 | Negative r is always | diverging | | 100 |
| 14374078945 | Converging mirror is | Concave | | 101 |
| 14374078946 | Diverging mirror is | Convex | | 102 |
| 14374078947 | Converging lens is | Convex | | 103 |
| 14374078948 | Diverging lens is | Concave | | 104 |
| 14374078949 | Index of refraction equation | n = c/v; where n is the index of refraction, c is the speed of light, and v is the new speed | | 105 |
| 14374078950 | Snell's Law | n1sin(Theta1) = n2sin(Theta2) | | 106 |
| 14374078951 | If n1>n2 | (Theta2 / Theta 1) must be >1 i.e. Theta 2 > Theta 1 --> Bends away from normal | | 107 |
| 14374078952 | If n1| (Theta2 / Theta 1) must be < 1 i.e. Theta 2 < Theta 1 --> Bends toward normal | | 108 | |
| 14374078953 | Critical Angle of incidence | Thetac = sin^-1(n2/n1); Can be derived from snell's law with Theta2 equal to 90 degrees | | 109 |
| 14374078954 | Lensmaker's Equation | (1/f) = (n-1) * [(1/r1)-(1/r2)] - Used when width of the lens is not negligable | | 110 |
| 14374078955 | Power of a lens equation | P = 1/f | | 111 |
| 14374078956 | index of refraction equation w/ regards to chromatic aberration | n = c/v; n = c / (lambda * f); in the new medium f is maintained, but lambda is changed. | | 112 |
| 14374078957 | Double Slit light fringes equation | dsin(theta) = m * lambda; where d is the distance between the slits, theta is the angle between 0th light fringe and the desired light fringe | | 113 |
| 14374078958 | Single Slit Dark Fringes equation | asin(theta) = m * lambda; where a is the slit length, theta is the angle between the 0th light fringe and the desired dark fringe | | 114 |
| 14374078959 | Thin Film Constructive interference formula (assuming pi shift i.e. n1| 2*n2*t = (m + .5)*lambda; where n2 is the index of which light is entering, t is the thickness of the film, m is the multiple of which constructive interference would occur, and lambda is the wavelength of light prior to entering | | 115 | |
| 14374078960 | Thin Film Destructive Interference Formula (Assuming pi shift i.e. n1| 2*n2*t = m*lambda; where n2 is the index of which light is entering, t is the thickness of the film, m is the multiple of which destructive interference would occur, and lambda is the wavelength of light prior to entering. | | 116 | |
| 14374078961 | Kinetic Energy of an electron from photoelectric effect | KEmax = E(photon) - W -> KEmax = hf(photon) - hf(threshold); Thus once f >f(t), the frequency of the photon is directly proportional to the KE of the resulting electron. Also can be written as KEmax = h(c/lambda) - hf(threshold) | | 117 |
