Mechanics, EM, thermodynamics, relativity, quantum, calculus — constants included.
Mechanics
| Formula | Variables | Description |
|---|---|---|
F = m · a | F=force(N), m=mass(kg), a=accel(m/s²) | Newton's Second Law |
W = F · d · cos θ | W=work(J), d=displacement | Work done by force |
KE = ½ m v² | KE=kinetic energy(J), v=velocity | Kinetic energy |
PE = m · g · h | g=9.81 m/s², h=height | Gravitational potential energy |
p = m · v | p=momentum(kg·m/s) | Linear momentum |
F_g = G · m₁m₂ / r² | G=6.674×10⁻¹¹ N·m²/kg² | Newton's Law of Gravitation |
v = v₀ + a·t | v₀=initial velocity | Kinematic: velocity |
x = x₀ + v₀t + ½at² | x=position | Kinematic: position |
v² = v₀² + 2a·Δx | — | Kinematic: velocity² |
T = 2π√(l/g) | T=period(s), l=length | Simple pendulum period |
Electromagnetism
| Formula | Description |
|---|---|
F = k · q₁q₂ / r² | Coulomb's Law (k=8.99×10⁹ N·m²/C²) |
V = I · R | Ohm's Law (V=volts, I=amps, R=ohms) |
P = V · I = I²R = V²/R | Electrical power |
C = Q / V | Capacitance (C=farads, Q=charge) |
E = ½ C V² | Energy stored in capacitor |
ε = −dΦ/dt | Faraday's Law of Induction |
c = 1/√(ε₀μ₀) ≈ 3×10⁸ m/s | Speed of light from Maxwell |
E = hf | Photon energy (h=6.626×10⁻³⁴ J·s) |
Thermodynamics
| Formula | Description |
|---|---|
ΔU = Q − W | First Law: energy conservation |
ΔS ≥ 0 | Second Law: entropy never decreases in isolated system |
PV = nRT | Ideal Gas Law (R=8.314 J/mol·K) |
η = 1 − T_cold/T_hot | Carnot efficiency |
Q = mcΔT | Heat (c=specific heat capacity) |
Special Relativity
| Formula | Description |
|---|---|
E = mc² | Mass-energy equivalence (c=3×10⁸ m/s) |
γ = 1/√(1 − v²/c²) | Lorentz factor |
t' = γ·t | Time dilation |
L' = L/γ | Length contraction |
Quantum Mechanics
| Formula | Description |
|---|---|
E = hf = hc/λ | Photon energy / wavelength |
λ = h/p | de Broglie wavelength (p=momentum) |
ΔxΔp ≥ ℏ/2 | Heisenberg Uncertainty Principle (ℏ=h/2π) |
Ĥψ = Eψ | Schrödinger's eigenvalue equation |
Algebra & Calculus
| Formula | Description |
|---|---|
(a+b)² = a² + 2ab + b² | Binomial square |
a² − b² = (a+b)(a−b) | Difference of squares |
x = (−b ± √(b²−4ac)) / 2a | Quadratic formula |
d/dx[xⁿ] = n·xⁿ⁻¹ | Power rule |
d/dx[eˣ] = eˣ | Derivative of eˣ |
d/dx[ln x] = 1/x | Derivative of ln |
∫xⁿ dx = xⁿ⁺¹/(n+1) + C | Power rule integration |
∫eˣ dx = eˣ + C | Integral of eˣ |
∑k (k=1 to n) = n(n+1)/2 | Sum of first n integers |
Constants
| Constant | Symbol | Value | Unit |
|---|---|---|---|
| Speed of light | c | 2.998 × 10⁸ | m/s |
| Gravitational constant | G | 6.674 × 10⁻¹¹ | N·m²/kg² |
| Planck constant | h | 6.626 × 10⁻³⁴ | J·s |
| Boltzmann constant | k_B | 1.381 × 10⁻²³ | J/K |
| Avogadro's number | N_A | 6.022 × 10²³ | mol⁻¹ |
| Electron charge | e | 1.602 × 10⁻¹⁹ | C |
| Electron mass | m_e | 9.109 × 10⁻³¹ | kg |
| Proton mass | m_p | 1.673 × 10⁻²⁷ | kg |
| Permittivity of free space | ε₀ | 8.854 × 10⁻¹² | F/m |
| Permeability of free space | μ₀ | 4π × 10⁻⁷ | H/m |
