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$\vec{F} = m \vec{a}$

$\sigma = \frac{F}{A}$

$\epsilon = \frac{\Delta L}{L_0}$

$E = \frac{\sigma}{\epsilon}$

$\tau = \frac{F}{A}$

$\frac{M}{I} = \frac{\sigma}{y} = \frac{E}{R}$

$\tau = r \times F$

$P = \frac{\Delta W}{\Delta t} = F v$

$\Delta L = \alpha L_0 \Delta T$

$Q = \frac{kA(T_1 - T_2)}{d}$

$Q = hA(T_s - T_\infty)$

$Q = \epsilon \sigma A(T^4 - T_\infty^4)$

$Re = \frac{\rho v L}{\mu}$

$P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}$

$\vec{p} = m \vec{v}$

$L = I\omega$

$I = \frac{1}{2} m r^2$

$K = \frac{1}{2} m v^2$

$K = \frac{1}{2} I \omega^2$

$W = F d \cos(\theta)$

$U = m g h$

$F = -kx$

$\Delta U = Q - W$

$PV = nRT$

$A_1 v_1 = A_2 v_2$

$MA = \frac{L_{effort}}{L_{load}}$

$C = \frac{Q}{V}$

$F_{cr} = \frac{\pi^2 E I}{(kL)^2}$

$h_f = \frac{f L v^2}{D 2g}$

$BHN = \frac{2P}{\pi D (D - \sqrt{D^2 - d^2})}$

$T = \dot{m} v_e + (p_e - p_0) A_e$

$D_h = \frac{4 A}{P}$

$Nu = \frac{h L}{k}$

$M = \frac{v}{a}$

$h = \frac{k}{L_c}$

$\sigma_{avg} = \frac{\sigma_x + \sigma_y}{2}$

$\Delta P = \frac{8 \mu L Q}{\pi R^4}$

$U_r = \frac{\sigma_y^2}{2E}$

$C_L = \frac{2L}{\rho v^2 A}$

$C_D = \frac{2D}{\rho v^2 A}$

$c_p = \frac{1}{m}\left(\frac{\Delta Q}{\Delta T}\right)_P$

$Fr = \frac{v}{\sqrt{g L}}$

$We = \frac{\rho v^2 L}{\sigma}$

$\epsilon_v = \Delta V / V_0$

$U_t = \int_0^{\epsilon_f} \sigma d\epsilon$