A-equations.tex

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\begin{document}
\chapter{Equations}
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\section{Equations to be learnt}
\subsection{Equations you need to remember for pre-U}

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\begin{longtable}{ll}
velocity & $v= \frac{\Delta x}{\Delta t}$ \\
acceleration & $a= \frac{\Delta v}{\Delta t}$ \\
resultant force & $F=ma$ \\
momentum & $p=mv$ \\
resultant force & $F=\frac{\Delta p}{\Delta t}$ \\
impulse & Impulse = change in momentum \\
density & Density = mass/volume \\
pressure & Pressure = force/area \\
pressure in a liquid & $P = \rho gh$ \\
weight & $W = mg$ \\
power & $P = Fv$ \\
GPE & $\Delta E = mg \Delta h$ \\
change in gravitational potential & $=g \Delta h $ \\
energy in a spring & $E = \frac{1}{2} Fx$ \\
efficiency & \% efficiency =
$\frac{\text{useful energy or power}}{\text{total energy or power in}}
\times 100$ \\
current & $I = \frac{\Delta Q}{\Delta t}$ \\
potential difference & $V = \frac{W}{Q}$ \\
resistance & $R = \frac{V}{I}$ \\
electrical power & $P = VI$ \\
electrical work done & $W = VIt$\\
resistance & $R = \frac{\rho l}{A}$ \\
resistors in series & $R_T = R_1 + R_2 + \ldots{}$\\
resistors in parallel &
\(\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \ldots\)\\
frequency & $f = 1/T$\\
wave speed & $v = f\lambda$\\
Malus' law & $\text{Intensity} \propto \cos^2{\theta}$\\
photoelectric equation & \(hf = \phi + \frac{1}{2}mv_{\max}^{2}\)\\
angular velocity & $v = r\omega$ \\
period & $T = 2\pi /\omega$\\
circular motion & $F = mv^2/r$\\
electric field strength & $E = F/Q$\\
capacitance & $C = Q/V$\\
field strength/potential & $E = -\frac{\text{d}V}{\text{d}{X}}$ \\
the ideal gas law & $pV = nRT$\\
Boltzmann factor & $e^{- \frac{E}{kT}}$ \\
activity & $A = -\frac{\ud N}{\ud t}$\\
luminous flux &\(F = \frac{L}{4\pi d^{2}}\)\\

Hubble's law &\(v \approx H_{0}d\)\\

Hubble time & $t = 1/H_{0}$\\

\end{longtable}

\subsection{Equations you need to remember for paper 3, part B, but not for any other part of the examination.}
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\begin{longtable}{ll}
moment of inertia & \(I = \Sigma mr^{2}\)\\
shm & \(\frac{d^{2}x}{dt^{2}} = - \omega^{2}x\)\\
& $x = A\cos{\omega t}$\\
\end{longtable}

\newpage
\section{Derivations}
\subsection{Equations you need to derive and remember for pre-U}

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\begin{longtable}{ll}
energy in a spring & $E = \frac{1}{2}kx^2$ \\
kinetic energy & $E = \frac{1}{2}mv^{2}$\\
emf & $E = I(R+r)$\\
emf & $E = V + Ir$\\
electrical power & $P = I^{2}R$\\
critical angle & $\sin{c} = 1/n$\\
centripetal acceleration & $a = v^{2}/r$\\
centripetal acceleration & $a = r\omega^2$\\
uniform electric field & $Fd = QV$\\
uniform electric field & $E = V/d$\\
energy in a capacitor & $W = \frac{1}{2}CV^2$\\
energy in a capacitor & $W = \frac{1}{2}\frac{Q^2}{C}$\\
electric field due to a point charge &
\(E = \ \frac{Q}{{4\pi\varepsilon_{0}r}^{2}}\)\\

Kepler's third law & $r^{3} \propto T^{2}$\\
gravitational field strength & \(g = \frac{\text{Gm}}{r^{2}}\)\\

radius of curvature of particle in B-field &
\(r = \frac{\text{mv}}{\text{BQ}}\) \\

Hall effect & $V = Bvd$\\

kinetic theory of gases & $pV = \frac{1}{3}Nm\langle c^2 \rangle$\\

activity of a source & $A = \lambda N$\\

activity at time t & $A = A_0\text{e}^{-\lambda t}$\\
half-life & \(t_{\frac{1}{2}} = \frac{ln2}{\lambda}\)\\
\end{longtable}


\subsection{Equations you need to derive for paper 3, part B, but not for any other part of the examination.}

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moment of inertia of a ring & $I = mr^2$\\

moment of inertia of a disc & $I = mr^{2}/2$\\

moment of inertia of a rod about one end & $I = ml^2/3$\\

moment of inertia of a rod about its centre & $I = ml^{2}/12$\\

velocity in shm & $v = -A\omega \sin{\omega t}$\\

acceleration in shm & $a = -A\omega^{2}\cos{\omega t}$\\

total energy in shm & $E = \frac{1}{2}mA^2\omega^2$\\

electric potential (from electric force) &
\(W = \frac{Q_{1}Q_{2}}{4\pi\varepsilon_{o}r}\)\\

hydrogen atom energy levels &\(E_{n} = \frac{- 13.6eV}{n^{2}}\)\\
\end{longtable}
\end{document}