Young's Modulus: $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$
Bulk Modulus: $B = \frac{\Delta P}{-\Delta V/V}$
Shear Modulus: $G = \frac{\text{Shear Stress}}{\text{Shear Strain}} = \frac{F/A}{x/h}$
Poisson's Ratio: $\sigma = -\frac{\text{lateral strain}}{\text{longitudinal strain}}$
Pressure: $P = \frac{F}{A}$
Pressure in fluid: $P = P_0 + \rho gh$
Pascal's Law: Pressure applied to enclosed fluid is transmitted undiminished.
Archimedes' Principle: Buoyant force $F_B = \rho_{fluid} V_{submerged} g$
Equation of Continuity: $A_1 v_1 = A_2 v_2$
Bernoulli's Equation: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$
Surface Tension: $T = \frac{F}{L}$
Excess Pressure in bubble: $\Delta P = \frac{2T}{R}$ (liquid drop), $\Delta P = \frac{4T}{R}$ (soap bubble)
Capillary Rise: $h = \frac{2T \cos \theta}{\rho gr}$
Viscosity (Stokes' Law): $F = 6\pi \eta rv$
Reynolds Number: $Re = \frac{\rho vd}{\eta}$

First Law of Thermodynamics: $\Delta U = Q - W$
Work Done: $W = \int P dV$
Specific Heat: $Q = mc\Delta T$
Molar Heat Capacity: $C_P - C_V = R$ (Mayer's relation)
Ratio of Specific Heats: $\gamma = C_P / C_V$
Isothermal Process: $PV = \text{constant}$ ($T = \text{constant}$), $W = nRT \ln(\frac{V_f}{V_i})$
Adiabatic Process: $PV^{\gamma} = \text{constant}$, $TV^{\gamma-1} = \text{constant}$, $P^{1-\gamma}T^{\gamma} = \text{constant}$
Isobaric Process: $W = P\Delta V$ ($P = \text{constant}$)
Isochoric Process: $W = 0$ ($V = \text{constant}$)
Efficiency of Heat Engine: $\eta = 1 - \frac{Q_C}{Q_H} = 1 - \frac{T_C}{T_H}$ (Carnot)
Coefficient of Performance (Refrigerator): $K = \frac{Q_C}{W} = \frac{T_C}{T_H - T_C}$

Displacement: $x(t) = A \sin(\omega t + \phi)$
Velocity: $v(t) = A\omega \cos(\omega t + \phi) = \omega \sqrt{A^2 - x^2}$
Acceleration: $a(t) = -A\omega^2 \sin(\omega t + \phi) = -\omega^2 x$
Angular Frequency: $\omega = \sqrt{\frac{k}{m}}$ (spring-mass), $\omega = \sqrt{\frac{g}{L}}$ (simple pendulum)
Time Period: $T = \frac{2\pi}{\omega}$
Total Energy: $E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2$