\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{Gifted} \pdfinfo{ /Title (physics-unit-2.pdf) /Creator (Cheatography) /Author (Gifted) /Subject (Physics Unit 2 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}{A3A3A3} \definecolor{LightBackground}{HTML}{F3F3F3} \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{Physics Unit 2 Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Gifted} via \textcolor{DarkBackground}{\uline{cheatography.com/20101/cs/5484/}}} \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}Gifted \\ \uline{cheatography.com/gifted} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 21st October, 2015.\\ Updated 12th May, 2016.\\ 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}{p{0.4977 cm} p{0.4977 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{2.1 Vectors in Two Dimensions}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Page 116 Questions 14-21} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Separate the vectors into components using trigonometry (sin and cos). Add all the x components and the y components together to get the x and y of the final vector. Use Pythagorean Theorem to determine the magnitude of the final vector. Finally, use tan to isolate for the direction (angle).} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{2.4 Newton's Law's in Two Dimensions}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Page 113 Questions 37-43} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Net force is always equal to the acceleration of an object multiplied by the mass of the object. When adding or subtracting forces, treat it the same as any other vector. Just keep in mind that it can be expressed as a combination of acceleration and mass.} \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}{2.6 String-and-Pully Problems}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Page 120 Questions 49-52} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{With strings and pulleys the most important thing to consider is which forces are pulling in which direction. All forces will either be aiding the motion of the system or resisting it. Newton's second law is used to determine the acceleration of the system. Then one of the objects is isolated and considered separately to determine forces of tension.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{2.2 Relative Motion}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Page 116 Questions 22-29} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Frame of Reference - A coordinate system relative to which motion is described or observed. \newline \newline Problems involving this concept are simply the same as adding vectors. Keep in mind that motions are independent of one another (x and y components).} \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}{Range Equation}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/gifted_1445464017_Screen Shot 2015-10-21 at 5.45.31 PM.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{This equation may only be used when there is no difference in height between where the object is launched and where it lands.} \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}{2.7 Uniform Circular Motion}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Page 120 Questions 53-57} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Uses the questions of centripetal acceleration to determine the acceleration that an object experiences towards the centre of a circle by moving around it. Note that this acceleration does not mean a change in speed, but rather a change of direction. Centripetal acceleration is always towards the centre of the circle.} \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}{2.3 Projectile Motion}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Page 117 Questions 30-36} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Behaves like a parabolic function. The connection between the horizontal plane and the vertical plane is time. You may be asked to calculate any of the following: \newline \newline Time, Horizontal Distance, Vertical Distance, Maximum Height, Final Velocity} \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}{2.5 The Inclined Plane}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Page 119 Questions 44-48} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Split the force of gravity into two components; parallel (pulling down the incline), and perpendicular (force pulling object into the inclined plane). Find the normal force using the perpendicular force of gravity. This normal force can then be used to calculate the force of friction when given a coefficient value.} \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}{2.8 Centripetal Force}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Page 121 Questions 58-63} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Centripetal force is a fictitious force. It is always caused by either normal force of an incline, or tension of an object. If the force is not balanced, the object will not be able to maintain a circular motion.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}