\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{Mon. (Monz gomz)} \pdfinfo{ /Title (movimiento-curvilineo.pdf) /Creator (Cheatography) /Author (Mon. (Monz gomz)) /Subject (Movimiento curvilineo 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}{10A8B3} \definecolor{LightBackground}{HTML}{F0F9FA} \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{Movimiento curvilineo Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Mon. (Monz gomz)} via \textcolor{DarkBackground}{\uline{cheatography.com/64672/cs/23741/}}} \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}Mon. (Monz gomz) \\ \uline{cheatography.com/monz-gomz} \\ \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 July, 2020.\\ Updated 21st July, 2020.\\ 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} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Movimiento circular uniforme}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{Cuando un objeto se mueve con rapidez constante describiendo una trayectoria circular (en torno a un centro).}}% Row Count 3 (+ 3) } \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}{Movimiento curvilineo}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1594783859_MCUA.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.14425 cm} x{2.65466 cm} p{0.77809 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Elementos del Movimiento Uniforme Circular}} \tn % Row 0 \SetRowColor{LightBackground} \{\{ac\}\}Periodo. & Tiempo que tarda un objeto en dar una revolución completa. & \{\{ac\}\}{\bf{T}} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \{\{ac\}\}Frecuencia. & Número de veces que da una revolución por unidad de tiempo. & \{\{ac\}\}{\bf{ƒ}} \tn % Row Count 6 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}---} \SetRowColor{LightBackground} \mymulticolumn{3}{x{5.377cm}}{La velocidad y la velocidad angular son constantes.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Más fórmulas}} \tn % Row 0 \SetRowColor{LightBackground} Periodo & \{\{ac\}\}{\bf{T = 2π/ω}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} Frecuencia & \{\{ac\}\}{\bf{ƒ=1/T}} \tn % Row Count 2 (+ 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}{Velocidad tangencial}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{La velocidad que apunta a un sitio diferente en las diferentes posiciones del objeto en movimiento.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Analizar imagen de arriba. Representados por V} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.33459 cm} x{1.64241 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de velocidad tangencial}} \tn % Row 0 \SetRowColor{LightBackground} Vtangencial = perímetro de círculo por n & \{\{ac\}\}{\bf{vt = 2πRn}} \tn % Row Count 2 (+ 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}{Datos de referencia}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{n = número de revoluciones por segundo.} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{2π radian = 360º} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{π = 3.14159} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{1 radian (π) = 57.296º} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{1 revolución = 2 radianes (π)} \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Radianes. Es una unidad de medida angular, es el ángulo subvenido por el arco de círculo cuya longitud es igual al radio.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.18528 cm} x{1.79172 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula para calcular el ángulo.}} \tn % Row 0 \SetRowColor{LightBackground} ángulo = longitud del arco / radio. & \{\{ac\}\}{\bf{ø = x / r}} \tn % Row Count 2 (+ 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}{Velocidad angular}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{La velocidad con la que un objeto cambia su ángulo en el tiempo.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Medida en radianes/segundos} \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}{Fórmula velocidad angular}} \tn % Row 0 \SetRowColor{LightBackground} Velocidad angular = cambio de ángulos / tiempo & \{\{ac\}\}{\bf{ω = (Ø1 - Ø2) / (t1 - t2)}} \tn % Row Count 3 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{rad / seg} \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}{Velocidad Angular Media}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Es la velocidad en un intervalo de tiempo dado a diferencia de la instantánea que es es un instante dado.% Row Count 3 (+ 3) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.63781 cm} x{2.33919 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de Velocidad Angular Media}} \tn % Row 0 \SetRowColor{LightBackground} V.M.A = suma de v.angulares entre 2 & \{\{ac\}\}{\bf{ωm = (ω2 + ω1) / 2}} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.88206 cm} x{1.09494 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de ángulo total girado}} \tn % Row 0 \SetRowColor{LightBackground} Ángulo total = v.a.m por tiempo & ø = ωmt \tn % Row Count 2 (+ 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}{Aceleración angular}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Es el cambio de la velocidad angular en el tiempo.% Row Count 1 (+ 1) } \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}{Aceleración angular}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1594814956_Ac_MCU.JPG}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.63781 cm} x{2.33919 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de aceleración angular}} \tn % Row 0 \SetRowColor{LightBackground} aceleración angular = diferencia de ω entre diferencia de tiempos & \{\{ac\}\}{\bf{α=(ω2 - ω1) / (t2 - t1)}} \tn % Row Count 4 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Puntos importantes de Aceleración Angular}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{La velocidad del objeto será mayor a cualquier otro punto en la cuerda.} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{El objeto recorre la misma distancia que cualquier otro punto en la cuerda.} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Se recorre la misma cantidad de ángulo en el mismo tiempo en cualquier punto.} \tn % Row Count 6 (+ 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}{Desplazamiento Angular}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Es la diferencia de un ángulo transcurrido con otro.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Unidad de medida: Radianes} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{3.03597 cm} x{1.94103 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de desplazamiento angular}} \tn % Row 0 \SetRowColor{LightBackground} D.A. = diferencia de ángulos transcurridos. & \{\{ac\}\}{\bf{Δø = ø2 - ø1}} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}