Physics Formulae/Equations for Properties of Matter

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Equations for Properties of Matter.

Friction

Normal Force	$f_{n}=\mathbf {f} \cdot \mathbf {n} \,\!$
Static Friction, lies tangent to the surface	$f\leqslant \mu _{s}f_{n}\,\!$
Kinetic Friction, lies tangent to the surface	$f=\mu _{k}f_{n}\,\!$
Drag Force, tangent to the path	$f=\mu _{d}\rho av^{2}/2\,\!$
Terminal Velocity	$v_{t}={\sqrt {\frac {2fg}{\mu _{d}\rho A}}}\,\!$
Energy dissipation due to Friction (sound, heat etc)	$\Delta E=f_{k}d\,\!$

Quantity (Common Name/s)	(Common) Symbol/s	Definining Equation	SI Units	Dimension
General Stress	$\sigma \,\!$	$\sigma =F/A\,\!$ F may be any force applied to area A	Pa = N m^-2	[M] [T] [L]^-1
General Strain	$\epsilon \,\!$	$\epsilon =\Delta D/D\,\!$ D = dimension (length, area, volume) $\Delta D\,\!$ = change in dimension	dimensionless	dimensionless
General Modulus of Elasticity	$E_{\mathrm {mod} }\,\!$	$E_{\mathrm {mod} }=\sigma /\epsilon \,\!$	Pa = N m^-2	[M] [T] [L]^-1
Yield Strength/	$\,\!$
Ultimate Strength	$\,\!$
Young's Modulus	$E,Y\,\!$	$Y={\frac {FL}{A\Delta L}}\,\!$	Pa = N m^-2	[M] [T] [L]^-1
Shear Modulus	$G\,\!$	$G={\frac {FL}{A\Delta x}}\,\!$	Pa = N m^-2	[M] [T] [L]^-1
Bulk Modulus	$B\,\!$	$B={\frac {P}{\Delta V/V}}\,\!$	Pa = N m^-2	[M] [T] [L]^-1

density	$\rho =\Delta m/\Delta V\,\!$
pressure	$p=\Delta F/\Delta A\,\!$
pressure difference	$\Delta p=\rho g\Delta y\,\!$
pressure at depth	$p=p_{0}+\rho gh\,\!$
barometer versus manometer
Pascal's principle
Archimedes' Principle
buoyant force	$F_{b}=m_{f}g\,\!$
gravitational force when floating	$F_{g}=F_{b}\,\!$
apparent weight	$weight_{app}=weight-F_{b}\,\!$
ideal fluid
equation of continuity	$R_{V}=Av=\,\!$ constant
Bernoulli's Equation	$p+{\frac {\rho }{2}}v^{2}+\rho gh=\,\!$ constant