\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{WhoooshBooosh} \pdfinfo{ /Title (unit-3-vce-physics.pdf) /Creator (Cheatography) /Author (WhoooshBooosh) /Subject (Unit 3 VCE Physics Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{8962A3} \definecolor{LightBackground}{HTML}{F7F5F9} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Unit 3 VCE Physics Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{WhoooshBooosh} via \textcolor{DarkBackground}{\uline{cheatography.com/145977/cs/39132/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}WhoooshBooosh \\ \uline{cheatography.com/whoooshbooosh} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Not Yet Published.\\ Updated 8th June, 2023.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{x{1.34379 cm} x{3.63321 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Newton's Laws of Motion}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{First Law:}} & Objects have inertia, i.e. a stationary object remains stationary, or a moving object keeps on moving at the same speed in the same direction, if there is no net force acting on it \tn % Row Count 7 (+ 7) % Row 1 \SetRowColor{white} {\bf{Second Law:}} & Acceleration of an object is directly proportional to and in the same direction as the net force on it, and inversely proportional to its mass. \{\{nl\}\} F`net` = {\emph{ma}} \tn % Row Count 13 (+ 6) % Row 2 \SetRowColor{LightBackground} {\bf{Third Law:}} & When object A exerts a force on object B, B exerts a force of the same magnitude in the opposite direction on A . \{\{nl\}\} {\emph{F}}`on A by B` = {\emph{-F}}`on B by A` \tn % Row Count 19 (+ 6) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Vector Addition}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686134426_images (1).png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.9908 cm} x{2.9862 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{SLM Constant Acceleration Equations}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Uses:}} & {\bf{ Equation}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} {\emph{v u a t}} & v = u + at \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} {\emph{v u t s}} & s = 1/2 (u + v) t \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} {\emph{u a t s}} & s = ut + 1/2 at\textasciicircum{}2\textasciicircum{} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} {\emph{v a t s}} & s = vt - 1/2 at\textasciicircum{}2\textasciicircum{} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} {\emph{v u a s}} & v\textasciicircum{}2\textasciicircum{} = u\textasciicircum{}2\textasciicircum{} + 2as \tn % Row Count 6 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{0.62655 cm} x{1.2531 cm} x{1.21133 cm} x{1.08602 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Interpreting Motion Grpahs}} \tn % Row 0 \SetRowColor{LightBackground} & {\bf{d - t}} & {\bf{v - t}} & {\bf{a - t}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} {\bf{Direct Reading}} & {\emph{d}} at any {\emph{t}} \{\{nl\}\} {\emph{t}} at any {\emph{d}} & {\emph{v}} at any {\emph{t}} \{\{nl\}\} {\emph{t}} at any {\emph{v}} & {\emph{a}} at any {\emph{t}} \{\{nl\}\} {\emph{t}} at any {\emph{a}} \tn % Row Count 5 (+ 4) % Row 2 \SetRowColor{LightBackground} {\bf{Gradient}} & \seqsplit{intsantaneous} velocity at any point \{\{nl\}\} {\emph{v}}`avg` between any two points & \seqsplit{instantaneous} \seqsplit{acceleration} \{\{nl\}\} {\emph{a}}`avg` & - \tn % Row Count 12 (+ 7) % Row 3 \SetRowColor{white} {\bf{Area under graph}} & - & change in position & change in velocity \tn % Row Count 16 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}----} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Einstein's Special Relativity}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Postulate One }} \{\{nl\}\} The Principle of Relativity & {\bf{ Postulate Two }} \{\{nl\}\} The Constancy of the Speed of Light \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} \{\{fa-leaf\}\} the laws of physics are the same in all inertial frames of reference (not just mechanics) & \{\{fa-leaf\}\} the speed of light is constant for all observers \tn % Row Count 10 (+ 6) % Row 2 \SetRowColor{LightBackground} \{\{fa-leaf\}\} there is no 'preferred' or 'correct' frames of reference & \{\{fa-leaf\}\} this implies a universal speed limit \tn % Row Count 14 (+ 4) % Row 3 \SetRowColor{white} & \{\{fa-leaf\}\} this has implications of simultaneity of events \tn % Row Count 17 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Time Dilation}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{t = t`0`}}γ} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{γ = 1 / √*1 - v\textasciicircum{}2\textasciicircum{}/c\textasciicircum{}2\textasciicircum{}} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{t`0`}} is proper time, {\emph{t}} is dilated time (larger than proper time), γ is the Lorentz Factor} \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Length Contraction}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{L = L`0`/γ = L`0`√1 - v\textasciicircum{}2\textasciicircum{}/c\textasciicircum{}2\textasciicircum{}}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{L`0` is proper length, L is contracted length (small than proper length), and γ is still Lorentz factor} \tn % Row Count 4 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Relativistic Energy}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686145523_Screenshot 2023-06-07 234504.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Magnetic Flux and Induced EMF}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686158930_Screenshot 2023-06-08 032821.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{AC Generators (Alternators)}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686159235_Screenshot 2023-06-08 033324.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Induced EMF and Energy}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686158732_Screenshot 2023-06-08 032451.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Lenz's Law}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686159019_Screenshot 2023-06-08 032950.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Transformer Equations}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Across step-up and step-down transformers}} & {\emph{V`1` / V`2` = N`1` / N`2` = I`2` / I`2`}} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{Where voltage and no. of turns are proportional to each other and current is inversely proportional.} \tn % Row Count 5 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{DC Generators}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686159326_Screenshot 2023-06-08 033502.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Circular Motion}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686139683_Screenshot 2023-06-07 220746.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Centripetal Acceleration}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{1. Draw diagram showing all forces} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{2. If required, resolve forces into components} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{3. There is always a net force towards centre of circular path} \tn % Row Count 4 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Useful equations: \{\{nl\}\} F`net` = {\emph{mv\textasciicircum{}2\textasciicircum{} / r}} \{\{nl\}\} {\emph{v = 2πr / T}} \{\{nl\}\} {\emph{a = v\textasciicircum{}2\textasciicircum{} / r = 4πr\textasciicircum{}2\textasciicircum{} / T = 4π\textasciicircum{}2\textasciicircum{}f\textasciicircum{}2\textasciicircum{}r}}} \tn % Row Count 7 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Motion at Bottom of Loop}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686139961_Screenshot 2023-06-07 221201.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Motion at Top of loop}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686139993_Screenshot 2023-06-07 221220.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.53827 cm} x{2.43873 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Energy}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Conservation of Energy}} \{\{nl\}\} in an isolated system, energy is transformed from one form to another, can neither be created nor destroyed & E`k` = 1/2{\emph{mv\textasciicircum{}2\textasciicircum{}}} \{\{nl\}\} E`g` = {\emph{mgΔh}} \tn % Row Count 8 (+ 8) % Row 1 \SetRowColor{white} {\bf{Hooke's Law}} \{\{nl\}\} force exerted by spring is directly proportional, but opposite in direction, to the spring's extension or compression & F`s` = -k{\emph{x}} \tn % Row Count 15 (+ 7) % Row 2 \SetRowColor{LightBackground} {\bf{Strain Potential Energy}} & E`s` = 1/2{\emph{kΔx\textasciicircum{}2\textasciicircum{}}} \tn % Row Count 17 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Gravity}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{ Newton's Law of Universal Gravitation }} & Gravitation is a force of attraction that acts between any two bodies. The gravitational force between two bodies is given by: \{\{nl\}\} {\emph{F = GMm/r\textasciicircum{}2\textasciicircum{}}} = {\emph{mg}} \tn % Row Count 8 (+ 8) % Row 1 \SetRowColor{white} {\bf{Gravitational Fields}} & Vector field, a physical quantity with value at each point in space, existing in any region with gravitational effect \{\{nl\}\} {\emph{g = f/M = GM/r\textasciicircum{}2\textasciicircum{}}} (N kg\textasciicircum{}-1\textasciicircum{}) {\bf{= a(m s\textasciicircum{}-1\textasciicircum{})}} \tn % Row Count 17 (+ 9) % Row 2 \SetRowColor{LightBackground} {\bf{Free Falling Objects}} & influenced only by gravity \{\{nl\}\} net force given by: {\emph{ΣF = mg}} \{\{nl\}\} {\emph{a = ΣF/g = mg/g = g}} \tn % Row Count 22 (+ 5) % Row 3 \SetRowColor{white} {\bf{Kepler's Law}} & {\emph{R\textasciicircum{}3\textasciicircum{}/T\textasciicircum{}2\textasciicircum{} = GM/4π\textasciicircum{}2\textasciicircum{}}} \tn % Row Count 24 (+ 2) % Row 4 \SetRowColor{LightBackground} {\bf{Work done}} & objects moving through constant gravitational field \{\{nl\}\} {\emph{E`g` = mgΔh}} \{\{nl\}\} total energy of object moving through gravitational field is constant, even though relative amounts of kinetic and gravitational potential energy may change \{\{nl\}\} area under gravitational field-distance graph gives energy change per kilo of mass \tn % Row Count 41 (+ 17) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.09034 cm} x{2.88666 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Electricity}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Electric Fields}} & vector fields occurring around charged objects \{\{nl\}\} fields exert a non-contact force, may be attractive or repulsive \tn % Row Count 6 (+ 6) % Row 1 \SetRowColor{white} {\bf{Force on Charged Particle}} & {\emph{F = qE}} \tn % Row Count 8 (+ 2) % Row 2 \SetRowColor{LightBackground} {\bf{Coulomb's Law}} & The electric force between two charges (q1, q2) is proportional to the product of the charges and inversely proportional to the square of the distance between them. \tn % Row Count 16 (+ 8) % Row 3 \SetRowColor{white} {\bf{Point Charges}} & {\emph{F = kq`1`q`2` / r\textasciicircum{}2\textasciicircum{}}} \{\{nl\}\} where a positive value of force represents repulsion \{\{nl\}\} {\emph{E = kQ / r\textasciicircum{}2\textasciicircum{} (N C\textasciicircum{}-1\textasciicircum{})}} \tn % Row Count 21 (+ 5) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{DC Motors (Split Ring Commutators)}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686158100_Screenshot 2023-06-08 031405.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wein Filter}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686158168_Screenshot 2023-06-08 031542.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Changing the flux by rotating a loop}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686159165_Screenshot 2023-06-08 033207.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Root Mean Square Voltage}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686159387_Screenshot 2023-06-08 033554.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Projectile Motion}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686139158_Screenshot 2023-06-07 215846.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Momentum}} \tn % Row 0 \SetRowColor{LightBackground} "mass in motion" & {\emph{p = mv}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} is a vector & {\emph{F`net` = Δp / Δt}} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{A net force on an object will cause a change in momentum (Impulse)} \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Conservation of Momentum}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{If two objects collide in an isolated system, momentum will be conserved} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{initial momentum = final momentum} \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Σ{\emph{p}}`initial` = Σ{\emph{p}}`final`} \tn % Row Count 4 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\emph{m}}`1`{\emph{u}}`1` + {\emph{m}}`2`{\emph{u}}`2` = {\emph{m}}`1`{\emph{v}}`1` + {\emph{m}}`2`{\emph{v}}`2`} \tn % Row Count 6 (+ 2) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{OR Σ{\emph{p}}`final`- Σ{\emph{p}}`initial` = Δp = 0} \tn % Row Count 7 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Impulse}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Impulse = F`net`Δ{\emph{t}} = {\emph{mΔv}} = Δp} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{is a vector} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{units are either N s\textasciicircum{}-1\textasciicircum{} OR kg m s\textasciicircum{}-1\textasciicircum{}} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{using this equation between two states gives us the average F`net`} \tn % Row Count 5 (+ 2) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{is area under force-time graph} \tn % Row Count 6 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Collisions}} \tn % Row 0 \SetRowColor{LightBackground} An isolated event (no external forces and momentum is conserved) involving 2 or more objects & {\bf{Elastic Collision}} momentum and energy is conserved \tn % Row Count 5 (+ 5) % Row 1 \SetRowColor{white} Usually interact (often strongly) for a short period of time & {\bf{Inelastic Collision}} momentum is conserved but energy is not (lost to usually heat and sound) \tn % Row Count 10 (+ 5) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Equal and opposite impulses are exerted on each other} \tn % Row Count 12 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Work}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Work(scalar) is the energy transferred to an object or transformed by the application of a force} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Work is done by a force on an object when it causes a displacement of an object in the direction of the force} \tn % Row Count 5 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{W = Fs}} \{\{nl\}\} {\emph{W = Fs }} cosθ*} \tn % Row Count 6 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Work done on an object: \{\{nl\}\} {\emph{W = F`net`s}}} \tn % Row Count 7 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{If the energy doesn't change, or force is perpendicular to displacement, no work is done on object} \tn % Row Count 9 (+ 2) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{is area under force-displacement graph} \tn % Row Count 10 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.69218 cm} x{3.28482 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Magnets}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Magnetic FIelds}} & vector fields, denser the lines means stronger the fields \{\{nl\}\} field lines go from north to south pole and never touch \{\{nl\}\} magnets are always dipole, can never be monopole \tn % Row Count 7 (+ 7) % Row 1 \SetRowColor{white} {\bf{Earth as a Magnet}} & The Earth is one large magnet – believed to be due to convection currents of molten metals in the outer core \{\{nl\}\} True geographic north pole is actually magnetic south pole \tn % Row Count 14 (+ 7) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Induced EMF in a Moving Conductor}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686158653_Screenshot 2023-06-08 032233.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Linear Particle Accelerators}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686157352_Screenshot 2023-06-08 030200.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Charged Particles in a Magnetic Field}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686157625_Screenshot 2023-06-08 030619.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Generating Voltage}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{We know electric currents can produce magnetic fields} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{The separation of charges in the falling rod is an induced electromotive force or induced voltage (or potential difference)} \tn % Row Count 5 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{The object needs to keep moving, or the magnetic field needs to be changing for charges to remain separated (to maintain an induced voltage)} \tn % Row Count 8 (+ 3) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Electromotive force (emf), is a source voltage} \tn % Row Count 9 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Transformers}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686159458_Screenshot 2023-06-08 033711.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Inclined Plane}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686136484_Screenshot 2023-06-07 211418.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Banked Turn Design Speed}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686139794_Screenshot 2023-06-07 220917.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Projectile Motion}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/whoooshbooosh_1686139328_Screenshot 2023-06-07 220137.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Projectile Range Formula}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{R = u\textasciicircum{}2\textasciicircum{}sin(20) / g}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{assuming symmetric motion} \tn % Row Count 2 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}