## The OGs
| Name | Symbol | SI Units | Dimension | Example |
| ----------- | ------ | -------- | --------- | -------------------------- |
| Mass | $m$ | kg | M | Person ~= 75 kg |
| Distance | $x$ | m | L | Radius of earth = 6,371 m |
| Time | $t$ | s | T | 1 nanocentury = 3 s |
| Current | $I$ | A | I | Mains outlet rating = 15 A |
| Temperature | $T$ | K | $\theta$ | Room temp = 300 K |
## Physics
| Name | Symbol | Equation | SI Units | Dimension | Example |
| ---------------------- | --------------- | ------------------------------ | -------------------------- | ------------------------------------------------------ | ------------------------ |
| Velocity | $v$ | $v =\dot{x}$ | ${} \mathrm{m / s} {}$ | L/T | Walking speed = 1.5 m/s |
| Acceleration | $g$ | ${} a = \dot{v} {}$ | ${} \mathrm{m / s^{2}} {}$ | ${} \mathrm{L / T^{2}} {}$ | Gravity = 9.8 m/s$^{2}$ |
| Force | $F$ | ${} F = ma {}$ | ${} \mathrm{N} {}$ | ${} \mathrm{ML / T^{2}} {}$ | Apple = 200g = 2 N |
| Energy<br>Work | $E
lt;br>$Wlt;br> | ${} W = \int Fdx {}$ | ${} \mathrm{J} {}$ | $\mathrm{ML^{2} / T^{2}}$ | Phone battery = 72 kJ |
| Power<br>Heat Transfer | $Plt;br>$Q$ | $P = \dot{W}$ | ${} \mathrm{W} {}$ | $\mathrm{ML^{2} / T^{3}}$ | Hand drill = 300 - 800 W |
| Stress<br>Pressure | $\sigmalt;br>$P$ | ${} \sigma = \frac{F}{A} {}$ | Pa | ${} \mathrm{M / LT^{2}} {}$ | Atmosphere = 100,000 Pa |
| Entropy | $S$ | ${} \Delta S = \frac{Q}{T} {}$ | J/K | $\mathrm{\frac{\text{ML}^{2}}{\text{T}^{2}\theta}}$ | Calculated not measured |
| Charge | $q$ | ${} \dot{q} = I {}$ | C | IT | 1 Ah = 3600 C |
| Voltage | $V$ | ${} P = VI {}$ | W/A | ${} \frac{\text{ML}^{2}}{\text{T}^{3}\text{I}} {}$ | US Outlet = 120 V |
| Resistance | $R$ | ${} V = IR {}$ | $\Omega$ | ${} \frac{\text{ML}^{2}}{\text{T}^{3}\text{I}^{2}} {}$ | Human body ~ 100 kOhms |
| Inductance | $L$ | ${} V = L \frac{di}{dt} {}$ | $H$ | $\frac{\text{ML}^{2}}{\text{T}^{2}\text{I}^{2}}$ | Clinical MRI: 50 Henry |
## Properties
| Name | Symbol | Equation | SI Units | Dimension |
| ---------------------------------------------- | -------------- | ------------------------------------------------------- | --------------------------------- | --------------------------------------- |
| Enthalpy | $h$ | $h = u + \frac{P}{\rho}$ | J | $\mathrm{ML^{2} / T^{2}}$ |
| Density | ${} \rho {}$ | ${} \rho = m /V {}$ | ${} \text{kg} / \text{m}^{3} {}$ | ${} \mathrm{M / L^{3}} {}$ |
| Viscosity | $\mu$ | ${} \tau_{x}=\mu \frac{ \partial u }{ \partial x } {}$ | ${} \mathrm{Pa \cdot s} {}$ | ${} \mathrm{\frac{M}{LT}} {}$ |
| Kinematic Viscosity / <br>Momentum diffusivity | $\nu$ | ${} \nu = \mu / \rho {}$ | ${} \mathrm{m^{2} / s} {}$ | $\mathrm{L^{2} / T}$ |
| Thermal Diffusivity | ${} \alpha {}$ | ${} \alpha = k / \rho {}$ | ${} \mathrm{m^{2} / s} {}$ | $\mathrm{L^{2} / T}$ |
| Heat Transfer Coefficient | $h$ | ${} R = \frac{1}{hA} {}$ | ${} \mathrm{\frac{W}{m^{2}K}} {}$ | ${} \mathrm{\frac{M}{T^{3}\theta}} {}$ |
| Thermal Conductivity | $k$ | ${} R = \frac{L}{kA} {}$ | ${} \mathrm{\frac{W}{mK}} {}$ | ${} \mathrm{\frac{ML}{T^{3}\theta}} {}$ |
| Specific Heat Capacity | ${} c {}$ | ${} \Delta U = mc\Delta T {}$ | ${} \mathrm{\frac{J}{kg~K}} {}$ | $\mathrm{\frac{L^{2}}{T^{2}\theta}}$ |
## Constants
| Name | Symbol | Value | SI Units |
| :-------------- | -------------- | --------------------------- | ------------------------------------------------- |
| Speed of light | $c$ | ${} 2.998\times 10^{8} {}$ | m/s |
| Stefan-Boltzman | ${} \sigma {}$ | ${} 5.670\times 10^{-8} {}$ | ${} \frac{\text{W}}{\text{m}^{2}\text{K}^{4}} {}$ |
| Earth gravity | $g$ | 9.81 | m/s$^{2}$ |
## Conversions
Multiply imperial value by the conversion factor to get metric
| Metric | | Conversion | Imperial |
| ------ | --: | ---------: | -------- |
| mm | = | 25.4 | in |
| m/s | = | 0.45 | mph |
| km | = | 1.61 | mi |
| kg | = | 0.45 | lbm |
| N | = | 4.5 | lbf |
| MPa | = | 145 | psi |
| Nm | = | 0.11 | in-lb |
| Nm | = | 1.4 | ft-lb |
| °C | = | -32+0.56 | °F |
| deg | = | 57.3 | rad |
![[Pasted image 20260426122103.png|500]]
Units hall of fame:
Pounds per kilogram (£/kg)