Dimensional Formulas

$\text{Force: } F = ma \quad [M^1 L^1 T^{-2}]$

$\text{Energy: } W = Fd \quad [M^1 L^2 T^{-2}]$

$\text{Power: } P = W/t \quad [M^1 L^2 T^{-3}]$

$\text{Pressure: } P = F/A \quad [M^1 L^{-1} T^{-2}]$

$\text{Momentum: } p = mv \quad [M^1 L^1 T^{-1}]$

$\text{Angular momentum: } L = mvr \quad [M^1 L^2 T^{-1}]$

$\text{Surface tension: } S = F/l \quad [M^1 L^0 T^{-2}]$

$\text{Viscosity: } \eta = F/(A \cdot dv/dx) \quad [M^1 L^{-1} T^{-1}]$

Error Propagation

$Z = A \pm B \implies \Delta Z = \Delta A + \Delta B$

$Z = \frac{A \cdot B}{C} \implies \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B} + \frac{\Delta C}{C}$

$Z = A^n \implies \frac{\Delta Z}{Z} = n \cdot \frac{\Delta A}{A}$

$Z = \frac{A^a \cdot B^b}{C^c} \implies \% \text{ error} = a(\%A) + b(\%B) + c(\%C)$

Unit Conversion

$n_2 = n_1 \left(\frac{M_1}{M_2}\right)^a \left(\frac{L_1}{L_2}\right)^b \left(\frac{T_1}{T_2}\right)^c \quad [M^a L^b T^c]$

Key Values

$G_\text{SI} = 6.67 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2} \quad \xrightarrow{\text{CGS}} \quad G_\text{CGS} = 6.67 \times 10^{-8}\ \text{dyne cm}^2\text{g}^{-2}$

$T = 2\pi\sqrt{\frac{L}{g}} \quad \text{(}k = 2\pi \text{ cannot be derived dimensionally)}$