Physics Formulas

Motion
\( \begin{array}{c} \vec{v}_{\text{f}} = \vec{v}_{\text{i}} + \vec{a}\Delta{t} \end{array} \)
\( \begin{aligned} {\vec{v}_{\text{f}}}^{2} &= {\vec{v}_{\text{i}}}^{2} + \text{2}\vec{a} {\cdot} \Delta{\vec{x}} \\ \text{or }\; {\vec{v}_{\text{f}}}^{2} &= {\vec{v}_{\text{i}}}^{2} + \text{2}\vec{a} {\cdot} \Delta{\vec{y}} \end{aligned} \)
\( \begin{aligned} \Delta{\vec{x}} &= \vec{v}_{\text{i}}\Delta{t} + \dfrac{1}{2}\vec{a}\left(\Delta{t}\right)^{2} \\ \text{or }\; \Delta{\vec{y}} &= \vec{v}_{\text{i}}\Delta{t} + \dfrac{1}{2}\vec{a}\left(\Delta{t}\right)^{2} \end{aligned} \)
\( \begin{aligned} \Delta{\vec{x}} &= \left(\dfrac{\vec{v}_{\text{i}} + \vec{v}_{\text{f}}}{2}\right)\Delta{t} \\ \text{or }\; \Delta{\vec{y}} &= \left(\dfrac{\vec{v}_{\text{i}} + \vec{v}_{\text{f}}}{2}\right)\Delta{t} \end{aligned} \)

Force
\( \begin{array}{c} f_{\text{k}} = \mu_{\text{k}}N \end{array} \)
\( \begin{array}{c} {f_{\text{s}}}^{\text{max}} = \mu_{\text{s}}N \end{array} \)
\( \begin{array}{c} \vec{F}_{\text{net}} = m\vec{a} \end{array} \)
\( \begin{array}{c} F = \dfrac{Gm_{1}m_{2}}{d^{2}} \end{array} \)
\( \begin{array}{c} \vec{F}_{\text{net}} = \dfrac{\Delta{\vec{p}}}{\Delta{t}} \end{array} \)
\( \begin{array}{c} \Delta{\vec{p}} = m\left(\vec{v}_{\text{f}} - \vec{v}_{\text{i}}\right) \end{array} \)
\( \begin{array}{c} \vec{p} = m\vec{v} \end{array} \)
\( \begin{array}{c} w = F_{\text{g}} = mg \end{array} \)

Work, energy, and power
\( \begin{array}{c} K = E_{\text{k}} = \dfrac{1}{2}mv^{2} \end{array} \)
\( \begin{array}{c} U = E_{\text{p}} = mgh \end{array} \)
\( \begin{array}{c} E_{\text{mech}} = E_{\text{k}} + E_{\text{p}} \end{array} \)
\( \begin{array}{c} P = \dfrac{W}{\Delta{t}} \end{array} \)
\( \begin{array}{c} W = F\Delta{x}\cos{\theta} \end{array} \)
\( \begin{aligned} W_{\text{net}} &= \Delta{K} \\ \text{or }\; W_{\text{net}} &= \Delta{E_{\text{k}}} \end{aligned} \)
\( \begin{array}{c} \Delta{K} = \Delta{E_{\text{k}}} = E_{\text{k,f}} - E_{\text{k,i}} \end{array} \)
\( \begin{aligned} W_{\text{nc}} &= \Delta{K} + \Delta{U} \\ &= \Delta{E_{\text{k}}} + \Delta{E_{\text{p}}} \end{aligned} \)
\( \begin{array}{c} P_{\text{avg}} = Fv_{\text{avg}} \end{array} \)

Waves, sound, and light
\( \begin{array}{c} v_{\text{avg}} = \dfrac{D}{\Delta{t}} \end{array} \)
\( \begin{array}{c} v = f\lambda \end{array} \)
\( \begin{array}{c} T = \dfrac{1}{f} \end{array} \)
\( \begin{array}{c} E = hf \end{array} \)
\( \begin{array}{c} E = h\dfrac{c}{\lambda} \end{array} \)
\( \begin{array}{c} n = \dfrac{c}{v} \end{array} \)
\( \begin{array}{c} n_{1}\sin{\theta_{1}} = n_{2}\sin{\theta_{2}} \end{array} \)
\( \begin{array}{c} \theta_{c} = \sin^{-1}\left(\dfrac{n_{2}}{n_{1}}\right) \end{array} \)
\( \begin{array}{c} f_{\text{L}} = \dfrac{v \pm v_{\text{L}}}{v \pm v_{\text{S}}}f_{\text{S}} \end{array} \)
\( \begin{aligned} E &= W_{0} + E_{\text{k,max}} \\ \text{where } E &= hf \\ \text{and } W_{0} &= hf_{0} \\ \text{and } E_{\text{k,max}} &= \dfrac{1}{2}m_{\text{e}}{v_{\text{max}}}^{2} \end{aligned} \)

Electromagnetism
\( \begin{array}{c} \phi = BA\cos{\theta} \end{array} \)
\( \begin{array}{c} \mathcal{E} = -N\dfrac{\Delta{\phi}}{\Delta{t}} \end{array} \)

Electrostatics
\( \begin{array}{c} Q = nq_{\text{e}} \end{array} \)
\( \begin{array}{c} F = \dfrac{kQ_{1}Q_{2}}{r^{2}} \end{array} \)
\( \begin{array}{c} \vec{E} = \dfrac{\vec{F}}{q} \end{array} \)
\( \begin{array}{c} E = \dfrac{kQ}{r^{2}} \end{array} \)
\( \begin{array}{c} V = \dfrac{W}{q} \end{array} \)

Electric circuits
\( \begin{array}{c} I = \dfrac{Q}{\Delta{t}} \end{array} \)
\( \begin{array}{c} R_{\text{s}} = R_{1} + R_{2} + R_{3} + \ldots \end{array} \)
\( \begin{array}{c} \dfrac{1}{R_{\text{p}}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}} + \dfrac{1}{R_{3}} + \ldots \end{array} \)
\( \begin{array}{c} R = \dfrac{V}{I} \end{array} \)
\( \begin{aligned} P &= VI \\ P &= I^{2}R \\ P &= \dfrac{V^{2}}{R} \end{aligned} \)
\( \begin{array}{c} E = P\Delta{t} \end{array} \)
\( \begin{array}{c} W = Vq \end{array} \)
\( \begin{array}{c} W = VI\Delta{t} \end{array} \)
\( \begin{array}{c} W = I^{2}R\Delta{t} \end{array} \)
\( \begin{array}{c} W = \dfrac{V^{2}\Delta{t}}{R} \end{array} \)
\( \begin{array}{c} \mathcal{E} = I\left(R + r\right) \end{array} \)
\( \begin{array}{c} P = \dfrac{W}{\Delta{t}} \end{array} \)

Alternating current
\( \begin{array}{c} I_{\text{rms}} = \dfrac{I_{\text{max}}}{\sqrt{2}} \end{array} \)
\( \begin{array}{c} V_{\text{rms}} = \dfrac{V_{\text{max}}}{\sqrt{2}} \end{array} \)
\( \begin{array}{c} P_{\text{avg}} = V_{\text{rms}}I_{\text{rms}} \end{array} \)
\( \begin{array}{c} P_{\text{avg}} = {I_{\text{rms}}}^{2}R \end{array} \)
\( \begin{array}{c} P_{\text{avg}} = \dfrac{{V_{\text{rms}}}^{2}}{R} \end{array} \)