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	$f =\mu_d\rho a v^2/2\,\!$
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	$E, Y \,\!$	$Y = \frac{F L}{A \Delta L} \,\!$	Pa = N m^-2	[M] [T] [L]^-1
Shear Modulus	$G \,\!$	$G = \Delta x/L\,\!$	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	$F_b = m_fg\,\!$
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	$p + \frac{\rho}{2} v^2 + \rho g h =\,\!$ constant

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