# Physics Formulary

> [!TIP]
>
> You'll often see $\vec{v}$ and $\vec{\dot x}$, and $\vec{a}$ and 
> $\vec{\ddot{x}}$.
>
> These are equal, but the latter forms, express better the relation
> between state space variables

## Hooke's Law (AKA Spring Formula)
$\vec{F} = -k\vec{x}$
- $k$: Spring Constant
- $\vec{x}$: vector of spring stretch from rest position
  
## Fluid drag
$\vec{F_D} = \frac{1}{2}b\vec{v}^2C_{D}A$
- $b$: density of fluid
- $v$: speed of object ***relative*** to the fluid
- $C_D$: drag coefficient
- $A$: cross section area

### Stokes Drag
$\vec{F_D} = -6 \pi R\mu \vec{v}$
- $\mu$: dynamic viscosity
- $R$: radius (in meters) of the sphere
- $\vec{v}$: flow velocity ***relative*** to the fluid

### Simplified Fluid Drag (Simplified Stokes Equation)
$\vec{F_D} = -b \vec{v}$
- $b$: simplified coefficient that has everything else
- $\vec{v}$: flow velocity ***relative*** to the fluid
##

## Newton force