\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{Jaco (brandenz1229)} \pdfinfo{ /Title (physics-midterm-1.pdf) /Creator (Cheatography) /Author (Jaco (brandenz1229)) /Subject (Physics MidTerm 1 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}{7D7777} \definecolor{LightBackground}{HTML}{F6F6F6} \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 MidTerm 1 Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Jaco (brandenz1229)} via \textcolor{DarkBackground}{\uline{cheatography.com/138824/cs/29292/}}} \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}Jaco (brandenz1229) \\ \uline{cheatography.com/brandenz1229} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 29th September, 2021.\\ Updated 29th September, 2021.\\ 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*}{4} \begin{tabularx}{3.833cm}{x{1.68217 cm} x{1.75083 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 1 Unit(s) / Mechanics / Sig-Figs / Vectors}} \tn % Row 0 \SetRowColor{LightBackground} Speed = (d/t) || (m/s) & d = distance : m = meters \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} & t = time : s = seconds \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{1 km = 1000 m} \tn % Row Count 5 (+ 1) % Row 3 \SetRowColor{white} 1 kg = 1000 g & mass = (kg) \tn % Row Count 6 (+ 1) % Row 4 \SetRowColor{LightBackground} 1 hour = 3600 seconds & time = (seconds) \tn % Row Count 8 (+ 2) % Row 5 \SetRowColor{white} 1 mile = 1.609 km & length = (meter) \tn % Row Count 9 (+ 1) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{Volume = 1 cm\textasciicircum{}3\textasciicircum{}} \tn % Row Count 10 (+ 1) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Sig Figs}}} \tn % Row Count 11 (+ 1) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{π = 3.14 (3 sigfig)} \tn % Row Count 12 (+ 1) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{π = 3.14159 (6 sigfig)} \tn % Row Count 13 (+ 1) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Density}} = (mass / volume) || (kg / m\textasciicircum{}3\textasciicircum{}) || (g / cm\textasciicircum{}3\textasciicircum{})} \tn % Row Count 15 (+ 2) % Row 11 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{√ = square root} \tn % Row Count 16 (+ 1) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Vector}} ({\bf{Displacement}}) = √(x)\textasciicircum{}2\textasciicircum{}+(y)\textasciicircum{}2\textasciicircum{}} \tn % Row Count 17 (+ 1) % Row 13 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Total distance}} = x + y} \tn % Row Count 18 (+ 1) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{Vector A = Vector B {\emph{if}} |Vector A| = |Vector B|} \tn % Row Count 19 (+ 1) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Magnitude}}: √(x)\textasciicircum{}2\textasciicircum{}+(y)\textasciicircum{}2\textasciicircum{} = (Answer in Units) : 1 Direction} \tn % Row Count 21 (+ 2) % Row 16 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Components of Vector}}} \tn % Row Count 22 (+ 1) % Row 17 \SetRowColor{white} Vector A = Ax + Ay & Ax = A ⋅ cos(Θ) \{\{nl\}\} Ay = A ⋅ sin(Θ) \tn % Row Count 25 (+ 3) % Row 18 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{A}} = √(A ⋅ cos(Θ))\textasciicircum{}2\textasciicircum{} + (A ⋅ sin(Θ))\textasciicircum{}2\textasciicircum{}} \tn % Row Count 26 (+ 1) % Row 19 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Θ = Angle} \tn % Row Count 27 (+ 1) % Row 20 \SetRowColor{LightBackground} x = cos(Θ) \{\{nl\}\} y = sin(Θ) & cos(Θ) = Ax / A \{\{nl\}\} sin(Θ) = Ay / A \tn % Row Count 29 (+ 2) % Row 21 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{tan(Θ) = (y / x) or (Ay / Ax) or (By / Bx)} \tn % Row Count 30 (+ 1) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{3.833cm}{x{1.68217 cm} x{1.75083 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 1 Unit(s) / Mechanics / Sig-Figs / Vectors (cont)}} \tn % Row 22 \SetRowColor{LightBackground} x = Î \{\{nl\}\} y = ĵ \{\{nl\}\} z = k̂ & Vector A = AxÎ + Ayĵ \{\{nl\}\} Vector B = BxÎ + Byĵ \tn % Row Count 3 (+ 3) % Row 23 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Vector R = Vector A + Vector B \{\{nl\}\} Vector R = (Ax + Bx)Î + (Ay + By)ĵ \{\{nl\}\} Vector R (direction) = (x)Î + (y)ĵ \{\{nl\}\} Vector R (magnitude) = √(x)Î\textasciicircum{}2\textasciicircum{} + (y)ĵ\textasciicircum{}2\textasciicircum{}} \tn % Row Count 7 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{p{0.3433 cm} p{0.3433 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Quadratic Formula}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{x = (-b +/- √b\textasciicircum{}2\textasciicircum{} - 4 ⋅ a ⋅ c ) / (2 ⋅ a)} \tn % Row Count 1 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{x{1.7165 cm} x{1.7165 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 2: Motion along A Straight Line}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{One Dimensional Motion}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{`Average Speed` = (total distance) / (time)} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{`Displacement` = Final Point - Initial Point} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Not Constant Velocity}}} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{`Average Velocity (V)` = (displacement / time)} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{`Average Velocity (V)` = (∆x / ∆t)} \tn % Row Count 6 (+ 1) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Instantaneous Velocity}} = derivative of the given equation \{\{nl\}\} {\bf{Instantaneous Velocity}} = ( (a-final) - (a-initial) ) / ( (t-final)-(t-initial) )} \tn % Row Count 10 (+ 4) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{∆t = (t-final) - (t-initial)} \tn % Row Count 11 (+ 1) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{∆x = (x-final) - (x-initial)} \tn % Row Count 12 (+ 1) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Acceleration}}} \tn % Row Count 13 (+ 1) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{∆V = (V-final) - (V-initial) \{\{nl\}\} {\bf{∆t}} = (t-final) - (t-initial)} \tn % Row Count 15 (+ 2) % Row 11 \SetRowColor{white} {\bf{Acceleration}} (a) = (∆V) / (∆t) \{\{nl\}\} {[}a is constant{]} & if a \textgreater{} 0 (positive) \{\{nl\}\} if a \textless{} 0 (negative) \tn % Row Count 19 (+ 4) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Instantaneous Acceleration}} = derivative of the given equation} \tn % Row Count 21 (+ 2) % Row 13 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Constant Acceleration}} \{\{nl\}\} = constant acceleration motion in 1D} \tn % Row Count 23 (+ 2) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{`V-final` = (a ⋅ t) + V-initial \{\{nl\}\} `V-final`\textasciicircum{}2\textasciicircum{} = (v-initial)\textasciicircum{}2\textasciicircum{} + 2 ⋅ a ( (t-final) - (t-initial) )} \tn % Row Count 26 (+ 3) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{∆x}} = (x-final) - (x-initial) \{\{nl\}\} {\bf{∆x}} = (v-average) ⋅ (seconds) \{\{nl\}\} {\bf{∆x}} = (1/2 ⋅ (V-final) + (V-initial) ) ⋅ t (seconds)} \tn % Row Count 29 (+ 3) % Row 16 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{`x-final` = 1/2 ( (V-initial) + (V-final) ) ⋅ t + (x-initial) \{\{nl\}\} `x-final` = x-initial + (V-initial) ⋅ t(seconds) + 1/2 ⋅ a ⋅ t\textasciicircum{}2\textasciicircum{}} \tn % Row Count 32 (+ 3) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{3.833cm}{x{1.7165 cm} x{1.7165 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 2: Motion along A Straight Line (cont)}} \tn % Row 17 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Gravity (g)}} = -9.8 m/s\textasciicircum{}2\textasciicircum{}} \tn % Row Count 1 (+ 1) % Row 18 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{V-final = (V-initial) + g * t (seconds)} \tn % Row Count 2 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{x{0.92691 cm} x{2.50609 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 3: 2D or 3D Motion}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{The Acceleration Vector}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} a = ∆V / ∆t & (v-final) = (v-initial) + ∆V \{\{nl\}\} ∆V = (v-final) - (v-initial) \{\{nl\}\} ∆V = (v-final) + (-(v-initial)) \tn % Row Count 5 (+ 4) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Constant Speed Changing Direction}}} \tn % Row Count 6 (+ 1) % Row 3 \SetRowColor{white} a = ∆V / ∆t & (v-final) = (v-initial) + ∆V \{\{nl\}\} ∆V = (v-final) - (v-initial) \tn % Row Count 9 (+ 3) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Projectile Motion}} \{\{nl\}\} two assumptions:} \tn % Row Count 10 (+ 1) % Row 5 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{1. The freefall acceleration (g) is constant}} \{\{nl\}\} {\bf{2. Air resistance is negligible}}} \tn % Row Count 12 (+ 2) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{y-direction}} = constant acceleration motion \{\{nl\}\} {\bf{x-direction}} = constant velocity motion \{\{nl\}\} \{\{nl\}\} Acceleration is only negative (y-direction) \{\{nl\}\} g = -9.8 m/s\textasciicircum{}2\textasciicircum{}} \tn % Row Count 16 (+ 4) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Constant Velocity Motion}}} \tn % Row Count 17 (+ 1) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{x = (x-initial) + (v {[}x-direction{]} ) ⋅ t} \tn % Row Count 18 (+ 1) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{V (y-direction) = (v-initial) {[}y-direction{]} + g ⋅ t} \tn % Row Count 20 (+ 2) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{(y-final) = (y-initial + (v-initial) {[}y-direction{]} ⋅ t + 1/2 ⋅ g ⋅ t\textasciicircum{}2\textasciicircum{}} \tn % Row Count 22 (+ 2) % Row 11 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{V (y-direction)\textasciicircum{}2\textasciicircum{} = (v-initial) {[}y-direction{]}\textasciicircum{}2\textasciicircum{} + 2 ⋅ g ( (y-final) - (y-initial) )} \tn % Row Count 24 (+ 2) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{V (y-direction) = (v-initial) {[}y-direction{]} + g ⋅ t} \tn % Row Count 26 (+ 2) % Row 13 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Trig Identity}}} \tn % Row Count 27 (+ 1) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{sin(ΘΘ) = sinΘcosΘ + cosΘsinΘ} \tn % Row Count 28 (+ 1) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Constant Speed Motion}} \{\{nl\}\} {\emph{velocity is always changing}}} \tn % Row Count 30 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{3.833cm}{x{0.92691 cm} x{2.50609 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 3: 2D or 3D Motion (cont)}} \tn % Row 16 \SetRowColor{LightBackground} r = radius & V = (2πr)\textasciicircum{}2\textasciicircum{} : 4π\textasciicircum{}2\textasciicircum{}r \tn % Row Count 1 (+ 1) % Row 17 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{T = time-period} \tn % Row Count 2 (+ 1) % Row 18 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{a = ∆V / ∆t : never zero \{\{nl\}\} ∆V = (V / r) · ∆r} \tn % Row Count 4 (+ 2) % Row 19 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Centripetal Acceleration}}} \tn % Row Count 5 (+ 1) % Row 20 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{Ac = (V\textasciicircum{}2\textasciicircum{}) / r \{\{nl\}\} Ac = (2πr)\textasciicircum{}2\textasciicircum{} / r \{\{nl\}\} Ac = 4π\textasciicircum{}2\textasciicircum{}r / T\textasciicircum{}2\textasciicircum{}} \tn % Row Count 7 (+ 2) % Row 21 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Tangential and Radial Acceleration}}} \tn % Row Count 8 (+ 1) % Row 22 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{Ac = a-rad} \tn % Row Count 9 (+ 1) % Row 23 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Vector A-total = Vector A-tangential + Vector A-radical \{\{nl\}\} A-total = √(A-tan)\textasciicircum{}2\textasciicircum{} + (A-rad)\textasciicircum{}2\textasciicircum{}} \tn % Row Count 11 (+ 2) % Row 24 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Relative Motion}}} \tn % Row Count 12 (+ 1) % Row 25 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{r ' = ( (v-initial) ⋅ t ) - (vector-r)} \tn % Row Count 13 (+ 1) % Row 26 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{Vector-r = √( (v-initial) ⋅ t)\textasciicircum{}2\textasciicircum{} + (r ')\textasciicircum{}2\textasciicircum{}} \tn % Row Count 14 (+ 1) % Row 27 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Vector-V ' = (v-final) - (v-initial)} \tn % Row Count 15 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{x{1.7165 cm} x{1.7165 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 4: Newtons Laws}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Superposition of Forces}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Vector-R = Vector-F1 + Vector-F2} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{N = Net Force} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Fx = N · cos(ϴ) \{\{nl\}\} Fy = N · sin(ϴ) & Rx = ∑Fx \{\{nl\}\} Ry = ∑Fy \tn % Row Count 6 (+ 3) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{R = √(Rx)\textasciicircum{}2\textasciicircum{} + Ry\textasciicircum{}2\textasciicircum{}} \tn % Row Count 7 (+ 1) % Row 5 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Newton's 1st Law}} \{\{nl\}\} No Force; No Acceleration; No Motion} \tn % Row Count 9 (+ 2) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Inertia:}} \{\{nl\}\} the tendency of an object to resist any attempt to change its velocity} \tn % Row Count 11 (+ 2) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{{\bf{Newton's 2nd Law}}} \tn % Row Count 12 (+ 1) % Row 8 \SetRowColor{LightBackground} Net Force = m · g & a (x-direction) = (Fx total) / mass \{\{nl\}\} a (y-direction) = (Fy total) / mass \tn % Row Count 16 (+ 4) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{tan(ϴ) = y / x} \tn % Row Count 17 (+ 1) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Newton's 3rd Law}}} \tn % Row Count 18 (+ 1) % Row 11 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Fn = Normal Force} \tn % Row Count 19 (+ 1) % Row 12 \SetRowColor{LightBackground} Fy = Fn - m · g · cos(ϴ) & Fx = m · g · sin(ϴ) \tn % Row Count 21 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{x{1.3732 cm} x{2.0598 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 5: Applying Newton's Laws}} \tn % Row 0 \SetRowColor{LightBackground} vector-F = m · a & Fx = m · ax \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} T = tension : friction & Fy= m · ay \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} y = T - m · g & Fr = Fn : Normal Force (Fn) \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} {\bf{No Friction}} & α = Coefficient \tn % Row Count 7 (+ 1) % Row 4 \SetRowColor{LightBackground} Fn = m · g & Fx = T1· cos(ϴ) + T2· cos(ϴ) \tn % Row Count 9 (+ 2) % Row 5 \SetRowColor{white} & Fy = T1· sin(ϴ) + T2· sin(ϴ) \tn % Row Count 11 (+ 2) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{{\bf{Friction}}} \tn % Row Count 12 (+ 1) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{3.833cm}}{Static Friction (fs): Object not in motion \{\{nl\}\} Kinetic Friction (fK): Object is in motion} \tn % Row Count 14 (+ 2) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{} \tn % Row Count 14 (+ 0) % Row 9 \SetRowColor{white} {\bf{Empirical Formula}} & μk: Coefficient of Kinetic Friction \{\{nl\}\} μs: Coefficient of Static Friction \{\{nl\}\} Static: fs ≤ μs · Fn \{\{nl\}\} Static: fk = μk · Fn \tn % Row Count 20 (+ 6) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{3.833cm}}{} \tn % Row Count 20 (+ 0) % Row 11 \SetRowColor{white} {\bf{Terminal Speed}} & Fr α v \tn % Row Count 22 (+ 2) % Row 12 \SetRowColor{LightBackground} & Fr α v\textasciicircum{}2\textasciicircum{} \tn % Row Count 23 (+ 1) % Row 13 \SetRowColor{white} {\bf{Uniform Circular Motion}} & Fc = m · ac : m · V\textasciicircum{}2\textasciicircum{} / r \tn % Row Count 25 (+ 2) % Row 14 \SetRowColor{LightBackground} {\bf{Vertical Circle}} & Top: Fy = -m · (V\textasciicircum{}2\textasciicircum{} / r) \{\{nl\}\} Bottom: Fy = μs * m · (g + V\textasciicircum{}2\textasciicircum{} / r) \{\{nl\}\} \{\{nl\}\} maxV = √(fs · r) / m \{\{nl\}\} maxV = √ μs · g · r \tn % Row Count 31 (+ 6) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{3.833cm}{x{1.3732 cm} x{2.0598 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Chapter 5: Applying Newton's Laws (cont)}} \tn % Row 15 \SetRowColor{LightBackground} {\bf{Top View}} & T · sin(ϴ) = m · ac \{\{nl\}\} ac = tan(ϴ) · g \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}