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

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