\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-final-cheat-sheet.pdf) /Creator (Cheatography) /Author (Jaco (brandenz1229)) /Subject (Physics Final 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 Final Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Jaco (brandenz1229)} via \textcolor{DarkBackground}{\uline{cheatography.com/138824/cs/30208/}}} \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 15th December, 2021.\\ Updated 15th December, 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*}{3} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Chapter 2: Motion along A Straight Line}} \tn % Row 0 \SetRowColor{LightBackground} s = speed & t = time \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} Total Distance & x`f`+x`i` \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{One Dimensional Motion}}} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} Distance & d = s⋅t \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} Displacement & x`f`-x`i` \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} Speed & (x`f`+x`i`) / (t`f`+`t`i`) \tn % Row Count 7 (+ 2) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Not Constant Velocity}}} \tn % Row Count 8 (+ 1) % Row 7 \SetRowColor{white} Average Velocity & (x`f`-x`i`) / (t`f`-`t`i`) \tn % Row Count 10 (+ 2) % Row 8 \SetRowColor{LightBackground} x↑: v+ \{\{nl\}\} x↓: v- \{\{nl\}\} x→: v=0 & a+: v↑ \{\{nl\}\} a-: v↓ \{\{nl\}\} a=0: v→ \tn % Row Count 13 (+ 3) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Instantaneous Acceleration}}} \tn % Row Count 14 (+ 1) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{(v`f`-v`i`) / (t`f`-`t`i`)} \tn % Row Count 15 (+ 1) % Row 11 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Constant Acceleration in 1D}}} \tn % Row Count 16 (+ 1) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{V`f` = V`i` + (a⋅t)} \tn % Row Count 17 (+ 1) % Row 13 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Constant Acceleration Final Distance}}} \tn % Row Count 18 (+ 1) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{X`f`= 1/2(V`f`-V`i`) ⋅ t} \tn % Row Count 19 (+ 1) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{X`f`= X`i` + (V`i`⋅ t) + 1/2(a ⋅ t)} \tn % Row Count 20 (+ 1) % Row 16 \SetRowColor{LightBackground} a = (V`f`-V`i`) / t & t = (V`f`-V`i`) / a \tn % Row Count 21 (+ 1) % Row 17 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{V`f` = V`i`⋅ a\textasciicircum{}2\textasciicircum{}} \tn % Row Count 22 (+ 1) % Row 18 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{V`f`\textasciicircum{}2\textasciicircum{} = V`i`\textasciicircum{}2\textasciicircum{} + 2⋅a (x`f`-x`i`)} \tn % Row Count 23 (+ 1) % Row 19 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{G`y` = -9.8 m/s} \tn % Row Count 24 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.93643 cm} x{2.04057 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Chapter 14: Periodic Motion}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Angular Frequency}} & w = 2πf \{\{nl\}\} 2π/T \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} {\bf{Frequency}} & f = 1 / T \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} {\bf{Period}} & T = 1 / f \tn % Row Count 4 (+ 1) % Row 3 \SetRowColor{white} {\bf{Restoring Force}} & F`x` = -kx \tn % Row Count 5 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Simple Harmonic Motion}}} \tn % Row Count 6 (+ 1) % Row 5 \SetRowColor{white} k = Spring Constant & x = displacement \tn % Row Count 7 (+ 1) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{m = mass} \tn % Row Count 8 (+ 1) % Row 7 \SetRowColor{white} {\bf{Displacement as function of time}} & x = Acos(wt + Θ) \tn % Row Count 10 (+ 2) % Row 8 \SetRowColor{LightBackground} {\bf{Velocity as function of time}} & v = -wAsin(wt + Θ) \tn % Row Count 12 (+ 2) % Row 9 \SetRowColor{white} {\bf{Acceleration as function of time}} & a = -w\textasciicircum{}2\textasciicircum{}Acos(wt + Θ) \tn % Row Count 14 (+ 2) % Row 10 \SetRowColor{LightBackground} {\bf{x`max`}} = A {[}Amplitude{]} & {\bf{-x`max`}} = A {[}Amplitude{]} \tn % Row Count 16 (+ 2) % Row 11 \SetRowColor{white} {\bf{v`max`}} = wA & {\bf{-v`max`}} = wA \tn % Row Count 17 (+ 1) % Row 12 \SetRowColor{LightBackground} {\bf{a`max`}} = w\textasciicircum{}2\textasciicircum{}A & {\bf{-a`max`}} = w\textasciicircum{}2\textasciicircum{}A \tn % Row Count 19 (+ 2) % Row 13 \SetRowColor{white} {\bf{Equation for Simple Harmonic Motion}} & a`x = - (k/m) x \tn % Row Count 21 (+ 2) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{k = restoring force} \tn % Row Count 22 (+ 1) % Row 15 \SetRowColor{white} {\bf{Angular Frequency for SHM}} & w = √k/m \tn % Row Count 24 (+ 2) % Row 16 \SetRowColor{LightBackground} {\bf{Frequency for SHM}} & f = w/2π \tn % Row Count 25 (+ 1) % Row 17 \SetRowColor{white} & f = 1/2π√k/m \tn % Row Count 26 (+ 1) % Row 18 \SetRowColor{LightBackground} {\bf{Period for SHM}} & T = 1/f \tn % Row Count 27 (+ 1) % Row 19 \SetRowColor{white} & T = 2π/w \tn % Row Count 28 (+ 1) % Row 20 \SetRowColor{LightBackground} & T = 2π√m/k \tn % Row Count 29 (+ 1) % Row 21 \SetRowColor{white} {\bf{Total Mechanical Energy}} (Constant) & E = 1/2mv`x`\textasciicircum{}2\textasciicircum{} + 1/2kx\textasciicircum{}2\textasciicircum{} \tn % Row Count 31 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{x{2.93643 cm} x{2.04057 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Chapter 14: Periodic Motion (cont)}} \tn % Row 22 \SetRowColor{LightBackground} & E = 1/2kA\textasciicircum{}2\textasciicircum{} \tn % Row Count 1 (+ 1) \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}{Chapter 6: Work and Kinetic Energy}} \tn % Row 0 \SetRowColor{LightBackground} 1km = 1000m & 1 kg = 1000g \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} {\bf{Dot Product}} & P = Power \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} A⋅B = \seqsplit{(A`i`⋅B`i`)+(A`j`⋅B`j`)} & t = s \tn % Row Count 4 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{Work = Force ⋅ distance} \tn % Row Count 5 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{W = F`x`⋅ distance} \tn % Row Count 6 (+ 1) % Row 5 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{W = F⋅cosΘ⋅distance} \tn % Row Count 7 (+ 1) % Row 6 \SetRowColor{LightBackground} K`E`: 1/2⋅m⋅v\textasciicircum{}2\textasciicircum{} & U = m⋅g⋅h \tn % Row Count 8 (+ 1) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{W`total` = K`E``f` - K`E``i`} \tn % Row Count 9 (+ 1) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{W`x` = F (cosΘ)⋅s || W`y` = F (sinΘ)⋅s} \tn % Row Count 10 (+ 1) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Constant Speed}}} \tn % Row Count 11 (+ 1) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Friction (opposite) = cos(180\textasciicircum{}o\textasciicircum{})} \tn % Row Count 12 (+ 1) % Row 11 \SetRowColor{white} P = F⋅v & P = (W/t) \tn % Row Count 13 (+ 1) % Row 12 \SetRowColor{LightBackground} P`av`= ΔW / Δt {[}Average Power{]} & if F→ \& s← = - W \tn % Row Count 15 (+ 2) % Row 13 \SetRowColor{white} if F↓ \& s→ = 0 & if F→ \& s→ = W \tn % Row Count 17 (+ 2) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Force Required to \{\{nl\}\} Stretch a spring}}} \tn % Row Count 18 (+ 1) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{F`x` = k ⋅ x} \tn % Row Count 19 (+ 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}{Chapter 13: Newton's Law of Gravitation}} \tn % Row 0 \SetRowColor{LightBackground} G`E`= 6.67⋅10\textasciicircum{}-11\textasciicircum{} & Earth Gravity Constant \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} R`E`= 6.38⋅10\textasciicircum{}6\textasciicircum{} m & Earth Radius \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} M`E`= 5.972⋅10\textasciicircum{}24\textasciicircum{} kg & Mass of Earth \tn % Row Count 5 (+ 2) % Row 3 \SetRowColor{white} g = 9.8 m/s; a`g` = 9.8 m/s & r - R`E` = h \tn % Row Count 7 (+ 2) % Row 4 \SetRowColor{LightBackground} F`g` = \seqsplit{(G`E`⋅m`1`⋅m`2`)} / (r\textasciicircum{}2\textasciicircum{}) & F`g` = m ⋅ a \tn % Row Count 9 (+ 2) % Row 5 \SetRowColor{white} w = m⋅g & s = r - R`E` cosΘ \tn % Row Count 10 (+ 1) % Row 6 \SetRowColor{LightBackground} {\bf{Gravitation and Spherically \{\{nl\}\} Symmetric Bodies}} & F`g` = (G`E`⋅m`E`⋅m) / (r\textasciicircum{}2\textasciicircum{}) \tn % Row Count 13 (+ 3) % Row 7 \SetRowColor{white} {\bf{Weight of the body at Earth's Surface}} & w = F`g` = (G`E`⋅m`E`⋅m) / (R`E`\textasciicircum{}2\textasciicircum{}) \tn % Row Count 16 (+ 3) % Row 8 \SetRowColor{LightBackground} {\bf{Acceleration due to Gravity}} & g = (G`E`⋅m`E`) / (R`E`\textasciicircum{}2\textasciicircum{}) \tn % Row Count 18 (+ 2) % Row 9 \SetRowColor{white} {\bf{Velocity of Earth}} & V`E`= 4/3πR`E`\textasciicircum{}2\textasciicircum{} = 1.08⋅10\textasciicircum{}21\textasciicircum{} m\textasciicircum{}3\textasciicircum{} \tn % Row Count 20 (+ 2) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Gravitational Potential Energy}}} \tn % Row Count 21 (+ 1) % Row 11 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{U = -(G`E`⋅m`E`⋅m) / (r)} \tn % Row Count 22 (+ 1) % Row 12 \SetRowColor{LightBackground} {\bf{WorkDone by Gravity}} & W`grav` = m⋅g(r`1`-r`2`) \tn % Row Count 24 (+ 2) % Row 13 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{W`grav` = Gm`E`⋅m ⋅ (r`1`-r`2`) / (r`1`⋅r`2`)} \tn % Row Count 26 (+ 2) % Row 14 \SetRowColor{LightBackground} W`grav`= Gm`E`⋅m ⋅ (r`1`-r`2`) / (R`E`\textasciicircum{}2\textasciicircum{}) & {[}if the body stays close to Earth{]} \tn % Row Count 29 (+ 3) % Row 15 \SetRowColor{white} {\bf{Speed of the Satellite}} & v = √(G⋅m`E` / r) \tn % Row Count 31 (+ 2) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Chapter 13: Newton's Law of Gravitation (cont)}} \tn % Row 16 \SetRowColor{LightBackground} {\bf{Period of Circular Orbit}} & T = (2πr / v) \tn % Row Count 2 (+ 2) % Row 17 \SetRowColor{white} T = 2πr\textasciicircum{}3/2\textasciicircum{}/√G⋅m`E` & T = 2πr √(r / G⋅m`E`) \tn % Row Count 4 (+ 2) % Row 18 \SetRowColor{LightBackground} {\bf{Point Mass Outside \{\{nl\}\} a Spherical Shell}} & U`i`= - Gm⋅m`i` / s \tn % Row Count 7 (+ 3) % Row 19 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Apparent weight \{\{nl\}\} ; Earth's Rotation}}} \tn % Row Count 8 (+ 1) % Row 20 \SetRowColor{LightBackground} w`0` = true weight of object & F = force exerted by spring scale \tn % Row Count 10 (+ 2) % Row 21 \SetRowColor{white} F + w`0` = net force on object & w = apparent weight = opposite of F \tn % Row Count 12 (+ 2) % Row 22 \SetRowColor{LightBackground} {\bf{centripetal acceleration}}` & w`0`- F = (mv\textasciicircum{}2\textasciicircum{} / R`E`) \tn % Row Count 14 (+ 2) % Row 23 \SetRowColor{white} & w = w`0` - (mv\textasciicircum{}2\textasciicircum{} / R`E`) \tn % Row Count 16 (+ 2) % Row 24 \SetRowColor{LightBackground} {\bf{freefall acceleration}} & g = g`0` - (v\textasciicircum{}2\textasciicircum{}/ R`E`) \tn % Row Count 18 (+ 2) % Row 25 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Black Holes}}} \tn % Row Count 19 (+ 1) % Row 26 \SetRowColor{LightBackground} P = Density & P = M / v \tn % Row Count 20 (+ 1) % Row 27 \SetRowColor{white} v = 4/3πR\textasciicircum{}3\textasciicircum{} & c = speed of light in the vaccum \tn % Row Count 22 (+ 2) % Row 28 \SetRowColor{LightBackground} {\bf{Schwardzschild Radius}} & R`s` = 2GM / c\textasciicircum{}2\textasciicircum{} \tn % Row Count 24 (+ 2) % Row 29 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{c = √2GM / R`S`} \tn % Row Count 25 (+ 1) \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}{Chapter 7: Potential Energy, Energy Conservation}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Y-axis}} \{\{nl\}\} E = Mechanical Energy} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{W`grav` = F ⋅ s = w(y`1`-y`2`)} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{\seqsplit{W`grav`=(m⋅g⋅y`1`)-(m⋅g⋅y`1`)}} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{W`grav`=U`grav,1` - U`grav,2`} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{W`grav` = -Δ U`grav`} \tn % Row Count 5 (+ 1) % Row 5 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Conservation \{\{nl\}\} of Mechanical Energy}}} \tn % Row Count 6 (+ 1) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{K`f`-K`i` = U`grav,1` - U`grav,2`} \tn % Row Count 7 (+ 1) % Row 7 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{K`i`+U`grav,1`=K`f`+U`grav,2`} \tn % Row Count 8 (+ 1) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{E = K + U`grav` = constant \{\{nl\}\} (if gravity does work)} \tn % Row Count 10 (+ 2) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{When other forces \{\{nl\}\} than Gravity do work}}} \tn % Row Count 11 (+ 1) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{W`other` + W`grav` = K`f` - K`i`} \tn % Row Count 12 (+ 1) % Row 11 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Elastic Potential Energy}}} \tn % Row Count 13 (+ 1) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{U`el` = 1/2kx\textasciicircum{}2\textasciicircum{}} \tn % Row Count 14 (+ 1) % Row 13 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Work Done a Spring}}} \tn % Row Count 15 (+ 1) % Row 14 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{W = 1/2kx`2`\textasciicircum{}2\textasciicircum{} - 1/2kx`1`\textasciicircum{}2\textasciicircum{}} \tn % Row Count 16 (+ 1) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{If Elastic does work, \{\{nl\}\} total mechanical energy \{\{nl\}\} is stored}}} \tn % Row Count 18 (+ 2) % Row 16 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{K`i`+U`el,1`=K`f`+U`el,2`} \tn % Row Count 19 (+ 1) % Row 17 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Situations with Both Gravitational \{\{nl\}\} and Elastic Potential Energy}}} \tn % Row Count 21 (+ 2) % Row 18 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{\seqsplit{K`1`+U`1`+W`other`=K`2`+U`2`}} \tn % Row Count 22 (+ 1) % Row 19 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{The work done by all forces other than \{\{nl\}\} the gravitational force or \{\{nl\}\} elastic force equals the change in \{\{nl\}\} total mechanical energy \{\{nl\}\} E = K + U of the system}}} \tn % Row Count 26 (+ 4) % Row 20 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{The Law of Conservation \{\{nl\}\} of Energy}}} \tn % Row Count 27 (+ 1) % Row 21 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{ΔU`int` = -W`other` \{\{nl\}\} ΔU`int` = internal energy} \tn % Row Count 29 (+ 2) % Row 22 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Force and Potential Energy}}} \tn % Row Count 30 (+ 1) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Chapter 7: Potential Energy, Energy Conservation (cont)}} \tn % Row 23 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{F`x`(x) = - dU(x) / dx} \tn % Row Count 1 (+ 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}{Chapter 14: Periodic Motion (cont.)}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{The Simple Pendelum}} (TSP) & L = pendulum length \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} {\bf{Angular Frequency TSP}} & w = √k/m \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} & w = √mg / L /m \tn % Row Count 5 (+ 1) % Row 3 \SetRowColor{white} & w = √g/L \tn % Row Count 6 (+ 1) % Row 4 \SetRowColor{LightBackground} {\bf{Frequency TSP}} & f = w/2π \tn % Row Count 7 (+ 1) % Row 5 \SetRowColor{white} & f = 1/2π √g/L \tn % Row Count 8 (+ 1) % Row 6 \SetRowColor{LightBackground} {\bf{Period TSP}} & T = 2π/w \tn % Row Count 9 (+ 1) % Row 7 \SetRowColor{white} & T = 1/f \tn % Row Count 10 (+ 1) % Row 8 \SetRowColor{LightBackground} & T = 2π√L/g \tn % Row Count 11 (+ 1) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{The Physical Pendulum}} (TPP)} \tn % Row Count 12 (+ 1) % Row 10 \SetRowColor{LightBackground} L = angular momentum & L = mvr \tn % Row Count 13 (+ 1) % Row 11 \SetRowColor{white} w = Angular Velocity & w = ΔΘ / Δt \tn % Row Count 14 (+ 1) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{(I)nertia = L / w} \tn % Row Count 15 (+ 1) % Row 13 \SetRowColor{white} {\bf{Angular Frequency TPP}} & w = √mgd / I \tn % Row Count 17 (+ 2) % Row 14 \SetRowColor{LightBackground} {\bf{Period TPP}} & T = 2π √ I / mgd \tn % Row Count 18 (+ 1) % Row 15 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Damped Oscillation}}} \tn % Row Count 19 (+ 1) % Row 16 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{b = Damping Constant} \tn % Row Count 20 (+ 1) % Row 17 \SetRowColor{white} {\bf{Displace of Damped}} & x = Ae\textasciicircum{}-b(2m)t\textasciicircum{} cost (wt + Θ) \tn % Row Count 22 (+ 2) % Row 18 \SetRowColor{LightBackground} {\bf{Angular Frequency of Damped}} & w' = √ (k/m) - (b\textasciicircum{}2\textasciicircum{} / 4m\textasciicircum{}2\textasciicircum{}) \tn % Row Count 24 (+ 2) % Row 19 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Force Oscillations and Resonance}}} \tn % Row Count 25 (+ 1) % Row 20 \SetRowColor{LightBackground} F`max` = Maximum Driving Force & k = constant restoring force \tn % Row Count 27 (+ 2) % Row 21 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{w`d` = Driving Angular Frequency} \tn % Row Count 28 (+ 1) % Row 22 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{A = F`max` / √(k-mw`d`\textasciicircum{}2\textasciicircum{})\textasciicircum{}2\textasciicircum{} + b\textasciicircum{}2\textasciicircum{}w`d`\textasciicircum{}2\textasciicircum{}} \tn % Row Count 29 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}