\input{../include.tex} \input{../units.tex} \begin{document} \title{IGCSE Physics Notes}\date{2007--2009} \maketitle \tableofcontents \listoffigures \listoftables \section{General Physics} \subsection{Length \& Time} \subsection{Speed, Velocity \& Acceleration} \subsection{Mass \& Weight} \subsection{Density} \[Density\,\left(\frac{g}{cm^{3}}\, or\,\frac{kg}{m^{3}}\right)=\frac{Mass\,\left(g\, or\, kg\right)}{Volume\,\left(cm^{3}\, or\, m^{3}\right)}\] \[\rho=\frac{M}{V}\] \[\rho_{\left(H_{2}O\right)}=1\pm0.1\frac{g}{cm^{3}}\] \subsection{Density of a Gas} \begin{figure}[!htbp] \includegraphics[scale=1.8]{gas_density} \caption{Using a round bottomed flask of known volume} \end{figure} \begin{enumerate} \item Take mass when empty (under vacuum). \item Let air in and take mass. \item The difference between the two masses is the mass of the air. \item $\rho=\frac{M_{\left(air\right)}}{V_{\left(flask\right)}}$ \end{enumerate} \subsection{Forces} \subsection{Energy, Work \& Power} \subsection{Pressure} \section{Pressure} \[Pressure\,\left(\frac{N}{m^{2}}\, or\, Pa\right)=\frac{Force\,\left(N\right)}{Area\,\left(m^{2}\right)}\] \[P=\frac{F}{A}\] \[1\, Pa=1\,\frac{N}{m^{2}}\] \[1\, bar=10^{5}\, Pa\] \subsection{Pressure in Liquids} Pressure in a liquid is directly proportional to depth. \[P=\frac{d}{100}\] \[P\propto d\] \[P=kd\] \[k=\frac{1}{100}\] \[P=\frac{F}{A}=\frac{\rho Vg}{A}=\rho gh\] \[P\,\left(pressure,\,\frac{N}{m^{2}}\right)=\rho\,\left(density,\,\frac{kg}{m^{3}}\right)\, g\,\left(gravity,\,\frac{N}{kg}\right)\, h\,\left(height,\, m\right)\] \[\frac{kg}{m^{3}}\times\frac{N}{kg}\times m=\frac{m\cdot kg\cdot N}{m^{3}\cdot kg}=\frac{N}{m^{2}}\] \begin{itemize} \item Liquids transmit pressure \item Solids transmit force \end{itemize} \begin{figure}[htbp!] \includegraphics[scale=2.5]{liquid_pressure} \caption{Liquids transmit pressure.} \end{figure} \begin{itemize} \item At X: \[F=1000\, N\] \[A=1\, m^{2}\] \[P=\frac{1000}{1}=1000\, Pa\] \item At Y: \[F=10,000\, N\] \[A=10\, m^{2}\] \item Overall effect is equilibrium: \[1000\, Pa\times10\, m^{2}=10,000\, N\] \end{itemize} \begin{figure}[htbp!] \includegraphics[scale=2.5]{magdeburg_hemispheres} Force on hemispheres from atmosphere: \[surface\, area=\pi d^{2}\approx0.3\, m^{2}\] \[\therefore F=P\times A=1\times10^{5}\,\frac{N}{m^{2}}\,\times0.3\, m^{2}=3\times10^{4}\, N\] \caption{The Magdeburg Hemispheres.} \end{figure} \begin{figure}[htbp!] \includegraphics[scale=2]{mercury_barometer} \caption{A mercury barometer.} \end{figure} \section{Thermal Physics} \subsection{Simple Kinetic Molecular Model of Matter} \begin{itemize} \item Evidence for kinetic theory: \begin{itemize} \item Brownian motion \item crystals \end{itemize} \item Pressure laws: \begin{itemize} \item liquids: $p=\rho gh$ \item gases: $p=\rho gh$ \end{itemize} \end{itemize} \subsubsection{Brownian Motion} Brownian Motion occurs when invisible molecules of a liquid or gas bombard a visible particle due to random thermal movement. If the visible particle is small enough (but still large enough to be clearly observed) it is seen to undergo Brownian Motion, i. e. a random mmoving around, on an unpredictable path, no net change of position. \includegraphics[scale=3.5]{brownian_motion}% \includegraphics[scale=3.5]{random_walk} This theory supports kinetic theory because it is the only complete explanation, and it involves molecules (and/or atoms). \subsubsection{Thermometers} \includegraphics{thermometer} \begin{description} \item[Calibration] \begin{itemize} \item we need 2 fixed points: \begin{itemize} \item 0\degc \item 100\degc \end{itemize} \item Place thermometer in: \begin{itemize} \item melting ice \item steam above boiling water \end{itemize} \end{itemize} \item[Linearity] allows us to fill in the scale \item[Sensitivity] the change in mercury level per change in temperature \item[Range] difference between the largest and smallest possile readings \end{description} \subsubsection{Thermocouples} \begin{itemize} \item Temperature difference across two ends of a wire produces a small voltage (potential difference) \item Connecting a sensitive voltmeter with a different type of wire allows us to measure this voltage \item The effect is not linear so a calibration table is required \end{itemize} \subsection{Thermal Properties} \subsection{Transfer of Thermal Energy} \section{Properties of Waves} \subsection{General Wave Properties} \subsection{Light} \subsection{Sound} \section{Electricity \& Magnetism} \subsection{Simple Phenomena of Magnetism} \subsection{Electrical Quantities} \subsection{Electric Circuits} \subsection{Dangers of Electricity} \subsection{Electromagnetic Effects} \subsection{Cathode Ray Oscilloscopes} \section{Atomic Physics} \subsection{Radioactivity} \subsection{The Nuclear Atom} \appendix \appendixpage \addappheadtotoc \section{Symbols, Units \& Definitions} \setlength\LTleft{0pt} \setlength\LTright{0pt} \begin{longtable}{@{\extracolsep{0.2\textwidth}}lc@{\extracolsep{0.3\textwidth}}c} \textit{Quantity} & \emph{Symbol(s)} & \emph{Unit(s)} \\\hline \endhead \sf length & $l,h,x\ldots$ & $\km,\meter,\cm,\mm$ \\ \sf area & $A$ & $\squaremeter,\squarecentimeter$ \\ \sf volume & $V$ & $\cubicmeter,\cubiccentimeter$ \\ \sf weight & $W$ & $\newton$ \\ \sf mass & $m,M$ & $\kg,\gram$ \\ \sf time & $t$ & $\hours,\minutes,\second$ \\ \sf density & $\rho$ & $\gramspercubiccentimeter,\kgpercubicmeter$ \\ \sf speed & $u,v$ & $\kmperhour,\meterspersecond,\cmpersecond$ \\ \sf acceleration & $a$ & $\meterspersecondsquared$ \\ \sf acceleration of free fall & $g$ & $\meterspersecondsquared$ \\ \sf force & $F$ & $\newton$ \\ \sf moment of force (torque) & $M,\tau,F$ & $\newtonmeter$ \\ \sf work done & $W,E$ & $\joule$ \\ \sf power & $P$ & $\watt$ \\ \sf pressure & $p$ & $\pascal,\newtonspermeterssquared$ \\ \sf atmospheric pressure & $p$ & $\millibar$ \\ \sf temperature & $\theta,t$ & $\celsius$ \\ \sf specific heat capacity & $c$ & $\joulespergramcelsius,\joulesperkgcelsius$ \\ \sf specific latent heat & $L$ & $\joulespergram,\joulesperkg$ \\ \sf frequency & $f$ & $\hertz$ \\ \sf wavelength & $\lambda$ & $\meter,\cm$ \\ \sf focal length & $f$ & $\meter,\cm$ \\ \sf refractive index & $n$ & (dimensionless) \\ \sf angle of incidence & $i$ & $\degree$ \\ \sf angle of reflection/refraction & $r$ & $\degree$ \\ \sf critical angle & $c$ & $\degree$ \\ \sf voltage/P.\ D. & $V$ & $\volt,\millivolt$ \\ \sf current & $I$ & $\amp,\milliamp$ \\ \sf charge & $Q$ & $\coulomb,\ampsecond$ \\ \sf e.\ m.\ f. & $E$ & $\volt$ \\ \sf resistance & $R$ & $\Omega$ \\ \end{longtable} \section{Equations Reference} \begin{multicols}{2} \paragraph{Speed} \[s = \frac{d}{t} \] \paragraph{Acceleration} \[a = \frac{\Delta v}{t}\] \paragraph{Weight} \[W = m \cdot g\] \paragraph{Density} \[\rho = \frac{m}{V}\] \paragraph{Hooke's Law} \[F = k \cdot x\] \paragraph{Newton's Second Law} \[F = m \times a\] \paragraph{Moment of a Force} \[M = F \times d\] \paragraph{Kinetic Energy} \[E = \frac{1}{2}mv^2\] \paragraph{Gravitation Potential Energy} \[E = m \cdot g \cdot h\] \paragraph{Work Done} \[\Delta W = F \cdot d\] \paragraph{Power} \[P = \frac{E}{t}\] \paragraph{Pressure} \[p = \frac{F}{A}\] \paragraph{Liquid Pressure} \[p = h \cdot \rho \cdot g\] \paragraph{Boyle's Law} \[p_1V_1 = p_2V_2\] \paragraph{Energy to Raise Temperature} \[E = m \cdot c \cdot \Delta T\] \paragraph{Energy to Change State} \[E = m \cdot l_f\] or \[E = m \cdot l_v\] \paragraph{Wave Equation} \[v = f \cdot \lambda\] \paragraph{Refractive Index} \[n = \frac{c_\mathrm{vaccum}}{c_\mathrm{material}}\] \paragraph{Snell's Law} \[n = \frac{\sin i}{\sin r}\] \paragraph{Critical Angle for TIR} \[\sin C = \frac{1}{n}\] \paragraph{Electric Circuits} \[V = I \cdot R\] \paragraph{Electric Power} \[P = V \cdot I\] \paragraph{Electric Energy Transfer} \[E = V \cdot I \cdot t\] \paragraph{Total Resistance in Series Circuits} \[R_\mathrm{total} = R_1 + R_2 + R_3 + \cdots\] \paragraph{Total Resistance in Parallel Circuits} \[\frac{1}{R_\mathrm{total}} = \frac{1}{R_1} + \frac{1}{R_2} \cdots\] or \[R_\mathrm{total} = \frac{R_1R_2}{R_1 + R_2}\] \paragraph{Voltage \& Coils in Transformers} \[\frac{V_p}{V_s} = \frac{N_p}{N_s}\] \paragraph{Voltage \& Current in Transformers} \[V_s \cdot I_s = V_p \cdot I_p\] \end{multicols} \end{document}