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Based SI Units
| Length | Mass | Time | Current | Temperature | Amount | Luminosity |
| Meters, m | Kilograms, kg | Seconds, s | Amperes, A | Kelvin, K | Moles, mol | Candela, cd |
Derived SI Units
| Area | 𝑚 ² | Force | Newton, N = (kgm)/s ² |
| Volume | 𝑚^3 | Pressure | Pascal, Pa = N/m ² |
| Velocity | m/s | Energy | Joules, J = 𝑁 ∗ 𝑚 |
| Acceleration | m/s ² | Power | Watts, W = J/s |
Conversion
| sin 30 | 1/2 | cos 30 | 0.9 | tan 30 | 1/2 |
| sin 45 | | cos 45 | | tan 45 | |
| sin 60 | 0.9 | cos 60 | 1/2 | tan 60 | 2 |
| 1 km | 0.62 miles | 1 mile | 1.6 km |
| 1 meter | 3.28 feet | 1 atm | 101325 Pa |
| 1 kg | 2.2 lbs | | |
Prefixes for Units
| Giga – G | Mega – M | Kilo – K | | Centi – c | Mili – m | Micro – μ | Nano – n |
| 10^9 | 10^6 | 10^3 | | 10^-2 | 10^-3 | 10^-6 | 10^-9 |
Electricity Equations
| Electric field | E = R/q₀ | |
| Electric field due to point charge | E = Kq/ r² | |
| Electrostatic force | F = Kq₁q₂/ r² | |
| Electric potential energy | kQq/r | |
| Electric potential | U/q = kQ/r
∆V = ∆U/q₀ | (ratio of charge’s electric potential energy to magnitude of charge itself) |
| Potential energy in capacitor | U = 1/2CV ² | |
| Magnitude of electric field | Fe/q = kQ/r ² | |
| Magnitude of uniform electric field | V/d (V=Ed) | |
Energy Equations
| 1st law of thermodynamics | change in total internal energy(U) = Q-W | |
| Elastic potential energy | U=1/2kx ²
Force=-kx | Area under Force*distance graph=work |
| Energy | E=F*d | capacity to do work (force*distance)=Joules |
| Kinetic energy formula | KE = 1/2 mv² | |
| Kinetic Energy of Ejected Electron | E = hf-W | w= work function, w=hf (threshold) |
| PE | mgh | |
| Spring PE | PE = 1/2 Kx² | |
Flow Equations
| Laminar flow/Poiseuille’s law | πr^4ΔP/8nL | n=viscosity |
| Turbulent flow | Nn/pD | N=constant, n=viscosity, p=density, D=diameter |
Force Equations
| Buoyant Force | 1)density x volume of fluid displaced x gravity
2)density of the fluid x Volume submerged x gravity | |
| Centripetal Force | Ac = V²/ r
Fc = mv²/ r | |
| Conservation of momentum | m₁v₁ + m₂v₂ = m₁v₁ + m₂v₂ | |
| Frictional Coefficient | U=Ff/Fn | U=coefficient of friction (kinetic or static)
static > kinetic |
| Hooke’s law | F = -Kx (K= spring const) | |
| Kinetic Friction | Fk = µkFn | |
| Static friction | Fs≤ µsFn | |
| Gravitation Force | F=Gmm/r ² | U=coefficient of friction (kinetic or static)
Fn=normal force
Causes Kinetic energy to be converted into heat energy |
| Law of gravitation | F=GM₁M₂/ r² | |
| Magnitude of electrostatic force between 2 charges | kqq/r^2 | |
| Momentum | p=mv | |
| Newtons second law | Fnet = ma | |
| Impulse | change in momentum=mass*change in velocity | |
| Torque | t = F x r
t = Flsinθ (l=length) | a force that causes rotation distance from center |
Gas Equations
| Internal energy of ideal gas | U = 3/2 nRT | |
| Kinetic Gas Theory | KE= 3/2 PV | |
Heat Equations
| Equilibrium gibbs energy | ∆G˚ = -RTlnKeq | |
| Gibbs free enegy | ∆G = ∆H – T∆S | |
| Heat Equation | Heat (q) = mcΔT | c is specific heat; or Q=mL if there is a phase change, L is heat of transformation |
| Latent heat | ∆Q = mL | |
| Thermal expansion | ΔL = ɑLΔT | alpha is coefficient of linear expansion, L is original length, and t is change in temp |
Kinematics Equations
| Distance formula | d=vt | |
| Vƒ = V¡ + at | |
| Vƒ² = V¡² + 2aΔx | |
| Find distance when given time and rate | Δx = V¡t + 1/2at² | |
| Δx = Vƒ- 1/2at² | |
| Δx = 1/2(V¡ + Vƒ)t | |
Lens Equations
| Critical angle | (Θ)= sin-1(n2/n1) | |
| Lensmakers equation | 1/f = 1/o + 1/i | |
| Lens slit systems with one slit | asinΘ=n wavelength | A is width, theta is angle, n is integer indicating number of the fringe |
| Lens slit system with multiple slits | dsinΘ=(n+½)wavelength | D is distance |
| Lenses where thickness can’t be neglected | 1/f=(n-1)(1/r1-1/r2) | N is index of refraction, r is radius of curvature of each lens |
| Magnification | m = -i/o | i = image o=object |
| Power of lenses | 1/f | Power is positive for converging and negative for diverging |
Light Equations
| Energy of a photon | E = hf = hc/wavelength | |
| Index of Refraction | n = c/v | c = 3×10^8
v = velocity wave |
| Snell’s law | n₁sinθ₁ = n₂sinθ₂ | |
Magnetic Equations
| Magnetic force | qvBsinΘ | Thumb towards velocity, fingers towards magnetic field, palm in direction of force |
| Magnetic force by external magnetic field (straight wire) | ILBsinΘ | |
| Magnitude of magnetic field | ᘈI/2πr, Circular its just ᘈI/2r | |
Sound Equations
| Doppler effect | f’=f[(v+-vd)/(v+-vs)] | numerator: listener moving towards +, denominator: source moving away + |
| Sound level | 10log I/Io | I- intensity of sound wave, Io is threshold of hearing |
| Speed of sound | radical(B/p) | B = bulk modulus, measure of the medium’s resistance to compression. p = density of medium |
Sound Waves Equations
| Open pipes/standing waves | Wavelength = 2L/n (Frequency = nv/2L) | L = length, n = number of half wavelengths |
| Closed pipes | wavelength = 4L/n (Frequency = nv/4L) | |
| Doppler effect | f = f (v±Vd)/ (v±Vs) | |
| Spring angular frequency | w= 2πf = √K/m | |
| Pendulum angular freqency | w = 2πf = √g/L | |
| Wave speed | v=fλ | |
| Wave frequency and period | f = 1/T | |
Temperature Equations
| Celsius to Kelvin | K=C+273 | |
| Farenheit to Celsius | C= 5/9 (F-32) | |
| Boiling point Celcius and Fahrenheit | 100, 180 | |
Voltage Equations
| Capacitance | q = VC | |
| Capacitors in parallel | Cp = C₁ + C₂ + etc | |
| Capacitors in series | 1/Cs = 1/C₁ + 1/C₂ + etc | |
| Energy stored by capacitor | U = 1/2CV² | |
| Current | I = ∆q/ ∆t (q = charge) | |
| Ohms law | P=IV
V=IR | (v = volts, I= current, R = resistance, P= power) |
| Magnetic force | F =qvBsinθ
F = ILBsinθ | |
| Magnetic force around wire | B = µ₀I/ 2πr | (I= current) |
| Magnetic field at center of wire loop | B = µ₀I/ 2r | |
| Resistors in parallel | 1/Rp = 1/R₁ + 1/R₂ + etc | |
| Resistors in series | Rs = R₁ + R₂ + etc | |
Water Equations
| Buoyant force | Fb = pVg | |
| Density | p = m/V | |
| Osmotic pressure | π = MRT | |
| Pressure | P = F/A | |
| Specific gravity | s.g = psub/ pwater | (p = density) |
| Total pressure of fluid | Ptot = Patm + Pgauge | |
Work Equations
| 1st law of thermo | ∆U = Q-W (work = W) | |
| Work | W=Fdcosθ
W =energy transferred (=change in energy)
W =area under P-V graph | |
| Power | P =work/time=Watts (joules/sec)
P =Force*velocity | |
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