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

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