38 lines
934 B
Markdown
38 lines
934 B
Markdown
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# Physics Formulary
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> [!TIP]
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>
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> You'll often see $\vec{v}$ and $\vec{\dot x}$, and $\vec{a}$ and
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> $\vec{\ddot{x}}$.
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>
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> These are equal, but the latter forms, express better the relation
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> between state space variables
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## Hooke's Law (AKA Spring Formula)
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$\vec{F} = -k\vec{x}$
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- $k$: Spring Constant
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- $\vec{x}$: vector of spring stretch from rest position
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## Fluid drag
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$\vec{F_D} = \frac{1}{2}b\vec{v}^2C_{D}A$
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- $b$: density of fluid
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- $v$: speed of object ***relative*** to the fluid
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- $C_D$: drag coefficient
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- $A$: cross section area
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### Stokes Drag
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$\vec{F_D} = -6 \pi R\mu \vec{v}$
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- $\mu$: dynamic viscosity
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- $R$: radius (in meters) of the sphere
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- $\vec{v}$: flow velocity ***relative*** to the fluid
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### Simplified Fluid Drag (Simplified Stokes Equation)
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$\vec{F_D} = -b \vec{v}$
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- $b$: simplified coefficient that has everything else
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- $\vec{v}$: flow velocity ***relative*** to the fluid
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##
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## Newton force
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