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# Physics Formulas

## Motion

• $$\vec{v}_{\text{f}} = \vec{v}_{\text{i}} + \vec{a}\Delta t$$
• \begin{align} {\vec{v}_\text{f}}^{2} &= {\vec{v}_\text{i}}^{2} +2\vec{a} \cdot \Delta \vec{x} \\ \text{or } {\vec{v}_\text{f}}^{2} &= {\vec{v}_\text{i}}^{2} + 2\vec{a} \cdot \Delta \vec{y} \end{align}
• \begin{align} \Delta \vec{x} &= \vec{v}_\text{i} \Delta t + \dfrac{1}{2} \vec{a} (\Delta t)^2 \\ \text{or } \Delta \vec{y} &= \vec{v}_\text{i} \Delta t + \dfrac{1}{2} \vec{a} (\Delta t)^2 \end{align}
• \begin{align} \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{align}

## Force

• $$f_{\text{k}} = \mu_{\text{k}}N$$
• $$f_{\text{s}}^{\;\text{max}} = \mu_{\text{s}}N$$
• $$\vec{F}_{\text{net}} = m\vec{a}$$
• $$F = \dfrac{Gm_{1}m_{2}}{d^{2}}$$
• $$\vec{F}_{\text{net}} = \dfrac{\Delta \vec{p}}{\Delta t}$$
• $$\Delta \vec{p} = m(\vec{v}_{\text{f}} - \vec{v}_{\text{i}})$$
• $$\vec{p} = m\vec{v}$$
• $$w = F_{\text{g}} = mg$$

## Work, energy and power

• $$K = E_{\text{k}} = \dfrac{1}{2}mv^2$$
• $$U = E_{\text{p}} = mgh$$
• $$E_{\text{mech}} = E_{\text{k}} + E_{\text{p}}$$
• $$P = \dfrac{W}{\Delta t}$$
• $$W = F\Delta x \cos\theta$$
• \begin{align} W_{\text{net}} &= \Delta K \\ \text{or } W_{\text{net}} &= \Delta E_{\text{k}} \end{align}
• \begin{align} \Delta K = \Delta E_{\text{k}} &= E_\text{k,f} - E_\text{k,i} \end{align}
• \begin{align}W_{\text{nc}} &= \Delta K + \Delta U \\ &= \Delta E_{\text{k}} + \Delta E_{\text{p}} \end{align}
• $$P_{\text{avg}} = Fv_{\text{avg}}$$

## Waves, sound and light

• $$v_{\text{avg}} = \dfrac{D}{\Delta t}$$
• $$v = f\lambda$$
• $$T = \dfrac{1}{f}$$
• $$E = hf$$
• $$E = h\dfrac{c}{\lambda}$$
• $$n = \dfrac{c}{v}$$
• $$n_{1}\sin \theta_{1} = n_{2}\sin \theta_{2}$$
• $$\theta_{c} = \sin^{-1}\left( \dfrac{n_{2}}{n_{1}} \right)$$
• $$f_{\text{L}} = \dfrac{v\pm v_{\text{L}}}{v\pm v_{\text{S}}} f_{\text{S}}$$
• \begin{align} 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{align}

## Electromagnetism

• $$\phi = BA \cos \theta$$
• $$\mathcal{E} = -N \dfrac{\Delta \phi}{\Delta t}$$

## Electrostatics

• $$Q = nq_{\text{e}}$$
• $$F = \dfrac{kQ_1Q_2}{r^2}$$
• $$\vec{E} = \dfrac{\vec{F}}{q}$$
• $$E = \dfrac{kQ}{r^2}$$
• $$V = \dfrac{W}{q}$$

## Electric circuits

• $$I = \dfrac{Q}{\Delta t}$$
• $$R_{\text{s}} = R_1 + R_2 + R_3 + \cdots$$
• $$\dfrac{1}{R_{\text{p}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \cdots$$
• $$R = \dfrac{V}{I}$$
• \begin{align} P & = VI \\ P & = I^2R \\ P & = \dfrac{V^2}{R} \end{align}
• $$E = P \Delta t$$
• $$W = Vq$$
• $$W = VI\Delta t$$
• $$W = I^2R\Delta t$$
• $$W = \dfrac{V^2\Delta t}{R}$$
• $$\mathcal{E} = I(R+r)$$
• $$P = \dfrac{W}{\Delta t}$$

## Alternating current

• $$I_{\text{rms}} = \dfrac{I_{\text{max}}}{\sqrt{2}}$$
• $$V_{\text{rms}} = \dfrac{V_{\text{max}}}{\sqrt{2}}$$
• $$P_{\text{avg}} = V_{\text{rms}}I_{\text{rms}}$$
• $$P_{\text{avg}} = {I_{\text{rms}}}^{2}R$$
• $$P_{\text{avg}} = \dfrac{{V_{\text{rms}}}^{2}}{R}$$
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