Definitions and Equations for General Physics
Mechanics
| Definitions | Equations | Similar Equations | Units |
|---|
| p ≡ m v | x(t) = x(0) + v(0) * t + a * t2 / 2 | θ(t) = θ(0) + ω(0) * t + α * t2 / 2 | |
| acentripetal = v2 / r | Σ F = dp/dt | Σ τ = dL/dt | |
| Fgravity = - m g j | F = - (∂U/∂x, ∂U/∂y, ∂U/∂z) | | N = kg m / s2 |
| Ffriction = μ FN | Δp = ∫ Fexternal dt | ΔL = ∫ τexternal dt | |
| Fspring = - k Δx | | | |
| Work = ∫ F ⋅ dx | ΔE = Workexternal | | J = N m |
| K ≡ m v ⋅ v / 2 | | | |
| P ≡ dE/dt | | | W = J / s |
| rcm ≡ ∫ r dm / M | | | |
| Fthrust = vexhaust dm/dt | | | |
| θ ≡ x / r | | | |
| ω ≡ dθ/dt | | | |
| α ≡ d2θ/dt2 | | | |
| I ≡ ∫ r ⋅ r dm | Iparallel axis = Icm + M d2 | | |
| L = r ⊗ p | | | |
| τ = r ⊗ F | | | |
Electricity and Magnetism
| Definitions | Equations | Similar Equations | Numbers / Units |
|---|
| ρ ≡ Q / V | V(x,y,z) = (1 / (4 π ε)) ∫ dq / r | V(x,y,z) = -G ∫ dm / r | V = J / C |
| σ ≡ Q / A | U = qtest V | U = mtest V | e = 1.60218 * 10-19 C |
| λ ≡ Q / L | E(x,y,z) = (1 / (4 π ε)) ∫ r dq / r3 | B = (μ / (4 π)) I ∫ dl ⊗ r / r3 | 1 / (4 π ε) ≈ 9 * 109 N m2 / C2 |
| Φ ≡ ∫ E ⋅ dA | Φclosed surface = qinside / ε | ∫closed surface dΦB = 0 | μ = 4 π * 10-7 T m / A |
| C ≡ Q / ΔV | 1 / Cseries = 1 / C1 + 1 / C2 | 1/ Rparallel = 1 / R1 + 1 / R2 | F = C / V |
| Cparallel = C1 + C2 | Rseries = R1 + R2 | |
| Ucapacitor = C ΔV2 / 2 | Uinductor = L I2 / 2 | |
| p ≡ q r | τdipole = p ⊗ E | τcurrent loop = μ ⊗ B | |
| μ ≡ n I A | Udipole = - p ⋅ E | Ucurrent loop = - μ ⋅ B | |
| R = V / I | R = ρ L / A | P = I V | Ω = V / A |
| I ≡ dq / dt | Σjunction I = 0 | Σclosed loop ΔV = 0 | A = C / s |
| qRC(t) = C V + b e - t / (R C) | | |
| F = q (E + v ⊗ B) | F = I ∫ dl ⊗ B | T = N / (A m) |
| ΦB ≡ ∫ B ⋅ dA | ∫closed loop B ⋅ ds = μ I | ∫closed loop E ⋅ ds = - dΦB/dt | |
| L ≡ ΦB / I | Vinductor = L dI/dt | | H = V s / A |
| T = 2 π / ω | q(t) = A cos (ω t + φ) | | |
| ν = 1 / T | ωLC = 1 / √ (L C) | ωpendulum = √ (g / l) | Hz = 1 / s |
Wave Mechanics
| Definitions | Equations | Similar Equations | Numbers / Units |
|---|
| k = 2 π / λ | y(t) = A cos (k x +- ω t + φ) | | |
| c = ω / k = λ ν | cstring = √(T/μ) | cair = √ (γ R T / M) | |
| ωbeat = ω1 - ω2 | | cem = 1 / √(μ ε) = 2.998 * 108 m/s | |
| I = P / A | νO = νS (c + uO) / (c - uS) | | |
| db ≡ 10 log(I / 10-12 W/m2) | ksame = n π / l | kmixed = n π / (2 l), n odd | |
| S = E ⊗ B / μ | E / B = c | | |
| <S> = E2 / (2 μ c) | | |
| Preflecton = 2 S / c | | Pa = N / m2 |
| n ≡ c / v | n1 sin θ1 = n2 sin θ2 | n1 sin θcritical = n2 | |
| M = - I / O | 1 / I + 1 / O = 1 / f | | |
| 1 / f = (n - 1) (1 / Renter - 1 / Rexit) | 1 / f = 2 / Rmirror | |
| Δpath length2 slit = d sin θ = m or (m + 1/2) λ | Δpath length = 2 dlattice sin θ | |
| resolution = 1.22 λ / daperture | | |
| e ΔVs = h ν - φ | E = h ν | p = h / λ | h = 6.626 * 10-34 J s |
| rn = n2 a0 / Z | | a0 = .529 * 10-10 m |
| En = - E0 Z2 / n2 | | E0 = 13.606 eV |
| λmax = 2.9 * 10-3 m / T | | eV = e J |
| Δx Δpx ≥ h / (4 π) | ΔE Δt ≥ h / (4 π) | |
Thermodynamics
| Definitions | Equations | Similar Equations | Numbers / Units |
|---|
| W = ∫ P dV | P V = n R T | P Vγadiabatic = constant | 0 C = 273.15 K |
| Q = m c ΔT = C ΔT | dE = dQ + dW | | NA = 6.022 * 1023 |
| Q = m L | | | R = NA kB = 8.314 J / (mol K) |
| Pconduction = k A dT/dx | Pradiation = σ A e T4 | σ = 5.67 * 10-8 W / (m2 K4)) |
| | | |
| <E>dof = kB T / 2 | | kB = 1.381 * 10-23 J / K |
| dE = dQ = n cv dT | cv = χ R / 2 | cp = cv + R | |
| γ ≡ = cp / cv | | | |
| dQ = n cp dT | | | |
| dS = dQ / T | ΔSengine = - ΔQh / Th + ΔQc / Tc | Qc / Qh = Tc / Th for Carnot | |
| ε = W / Qh = 1 - Qc / Qh | | | |
| S = kB ln Ω | | | |
©2011, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.
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