Physics Formulas | Siyavula

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

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