Physics Constants & Extended Newtonian/General Reference

$v=v_0+at$, \; $x=x_0+v_0 t+\tfrac12 a t^2$, \; $v^2=v_0^2+2a\,\Delta x$, \; $\Delta x=\tfrac{(v+v_0)}{2}t$
Projectile: $x=v_0\cos\theta\,t$, \; $y=v_0\sin\theta\,t-\tfrac12 g t^2$; \; $R=\dfrac{v_0^2\sin2\theta}{g}$; \; $H=\dfrac{v_0^2\sin^2\theta}{2g}$; \; $t_f=\dfrac{2v_0\sin\theta}{g}$

$a_c=\dfrac{v^2}{r}=\omega^2 r$, $v=\omega r$, $T=\dfrac{2\pi}{\omega}$\; /\; $\omega=\omega_0+\alpha t$, $\theta=\theta_0+\omega_0 t+\tfrac12\alpha t^2$, $\omega^2=\omega_0^2+2\alpha\,\Delta\theta$
Torque $\tau=\vec r\times\vec F$, $\sum\tau=I\alpha$; \; $L=I\omega$, $\tfrac{d\vec L}{dt}=\sum\tau$; \; $K=\tfrac12 m v^2+\tfrac12 I\omega^2$; Parallel‑axis $I=I_\text{CM}+Md^2$

$W=\int \vec F\cdot d\vec r$, $K=\tfrac12 m v^2$, $U=mgh$ (near Earth), $W_{\text{net}}=\Delta K$, $P=\dfrac{dW}{dt}=\vec F\cdot\vec v$
$\vec p=m\vec v$, $\vec J=\int \vec F\,dt=\Delta\vec p$; perfectly inelastic $v_f=\dfrac{m_1v_1+m_2v_2}{m_1+m_2}$

$F=G\dfrac{m_1m_2}{r^2}$, $U=-G\dfrac{Mm}{r}$, $v_\text{esc}=\sqrt{\dfrac{2GM}{r}}$, circular $v=\sqrt{\dfrac{GM}{r}}$, $T=2\pi\sqrt{\dfrac{r^3}{GM}}$
Vis‑viva: $v^2=GM\left(\dfrac{2}{r}-\dfrac{1}{a}\right)$; Kepler 3rd: $T^2=\dfrac{4\pi^2}{GM}a^3$ (for $M\gg m$)

Continuity: $A_1 v_1 = A_2 v_2$ (incompressible 1‑D streamtube)
Bernoulli: $\underbrace{p}_{\text{static}}+\underbrace{\tfrac12\rho v^2}_{\text{dynamic}}+\underbrace{\rho g h}_{\text{hydrostatic}}=\text{const along streamline}$

Torricelli efflux: $v_\text{out}=\sqrt{2g\,\Delta h}$; Dynamic pressure: $q=\tfrac12\rho v^2$; Venturi: $\Delta p=\tfrac12\rho (v_2^2-v_1^2)$
Reynolds number: $\mathrm{Re}=\dfrac{\rho v D}{\mu}$ (laminar $\lesssim 2300$)

Ideal gas: $pV=nRT=Nk_B T$; \; Boyle: $p\propto 1/V$ (isothermal); \; Charles: $V\propto T$ (isobaric); \; Gay‑Lussac: $p\propto T$ (isochoric)
Dalton partial pressures: $p_\text{tot}=\sum_i p_i$ with $p_i=\chi_i p_\text{tot}$; \; van der Waals (real gas): $\left(p+\dfrac{a n^2}{V^2}\right)(V-nb)=nRT$

Amount: $n=\dfrac{m}{M}$ (mass / molar mass); \; Molarity: $M=\dfrac{n}{V}$ (mol L$^{-1}$)
pH: $\mathrm{pH}=-\log_{10}[\mathrm{H}^+]$, \; $K_w=[\mathrm{H}^+][\mathrm{OH}^-]=10^{-14}$ (25°C)

Kepler 3rd (two‑body, $M\gg m$): $T^2=\dfrac{4\pi^2}{GM}a^3$; \; Wien’s law: $\lambda_{\max}\,T\approx 2.898\times10^{-3}$ m·K; \; Magnitudes: $m_2-m_1=-2.5\log_{10}(F_2/F_1)$

$\dfrac{d\ln p}{dT}=\dfrac{L}{RT^2}$ (phase‑change regions)