\documentclass[10pt,a4paper]{article}

% Packages
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\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
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\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{liviabrookes}
\pdfinfo{
  /Title (mechanics.pdf)
  /Creator (Cheatography)
  /Author (liviabrookes)
  /Subject (Mechanics Cheat Sheet)
}

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% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
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% 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{Mechanics Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{liviabrookes} via \textcolor{DarkBackground}{\uline{cheatography.com/164261/cs/35193/}}}
\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}liviabrookes \\
  \uline{cheatography.com/liviabrookes} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 4th November, 2022.\\
   Updated 4th November, 2022.\\
   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{1.14471 cm} x{3.83229 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Speed, Distance, Time}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Speed}} & measured in metres per second, ms-1 \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Distance}} & measured in metres, m \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Time}} & measured in seconds, s, a measure of how long something takes \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
{\bf{D=VxT}} & distance = velocity x time \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Distance Time Graphs}}} \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-line upwards=getting farther away} \tn 
% Row Count 10 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{-line downwards=getting closer} \tn 
% Row Count 11 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-flat line=staying still} \tn 
% Row Count 12 (+ 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}{Force}}  \tn
% Row 0
\SetRowColor{LightBackground}
force = mass x acceleration & Fnet=ma \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
-{\bf{weight}} is a force measured in Newtons which changes depending on where you are eg. Earth vs. Mars & -{\bf{mass}} is the amount of matter contained in an object measured in kilograms. \tn 
% Row Count 8 (+ 6)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Effect of doubling the mass or force}}} \tn 
% Row Count 9 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-if you double the mass but keep the force the same, acceleration will be halved} \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{-if you double the force, acceleration will be doubled} \tn 
% Row Count 13 (+ 2)
\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}{Work}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{the measure of energy transfer when an object is moved over a distance}}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{W=Fd}}} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Work (J) = Force (N) x Distance (m)} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{When work is done to an object, the object gains energy} \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{When an object does work, it loses energy} \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\emph{work done=energy lost or gained}}} \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{The Ramp Question}}} \tn 
% Row Count 9 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{If one ball is thrown up a ramp and the other is dragged up, both balls will gain the same amount of gravitational potential energy assuming they are lifted to the same height, so the work done will be equal, assuming no energy is lost as heat and sound.} \tn 
% Row Count 15 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.44333 cm} x{3.53367 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{\seqsplit{Acceleration/Decceleration}}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Acceleration}} & a measure of how fast your speed is increasing, symbol is 'a', measured in ms-2 \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Deceleration}} & a measure of how fast your speed is decreasing \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Speed Time Graphs}}} \tn 
% Row Count 6 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-line upwards=constant acceleration} \tn 
% Row Count 7 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{-line downwards=constant deceleration} \tn 
% Row Count 8 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-flat line=constant speed} \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{-area under the graph=distance travelled} \tn 
% Row Count 10 (+ 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}{Friction and Pressure}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{friction is caused when things rub against each other}}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
-friction transfers kinetic energy into heat and sound energy & -friction increases when rougher or larger surfaces contact \tn 
% Row Count 6 (+ 4)
% Row 2
\SetRowColor{LightBackground}
-friction ALWAYS opposes motion & -it is measured in Newtons, N \tn 
% Row Count 8 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Air Resistance}} is a form of friction affecting all objects moving through the air} \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Terminal Velocity}} occurs when forces become equal and opposite so they are their constant, maximum speed} \tn 
% Row Count 13 (+ 3)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Eg. when a parachute opens the force of air resistance increases because the surface area has increased. This causes the parachuter to decelerate.} \tn 
% Row Count 16 (+ 3)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{pressure is a force spread over an area}}} \tn 
% Row Count 17 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{High Pressure}} is a force spread over a small area} \tn 
% Row Count 19 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Low Pressure}} is a force spread over a large area} \tn 
% Row Count 21 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{P=F/A where P is measured in Pa, F is N, and A is ㎡.} \tn 
% Row Count 23 (+ 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}{Power}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{*the speed at which work is done} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{P=W/T}} where P is measured in W, W is J, T is s} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{eg. if you walk up stairs slowly or quickly the same amount of work has been done. However, doing it faster means you have used more power.} \tn 
% Row Count 5 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Unrelated to Power}} \newline -1/2 the acceleration means twice the mass \newline -Acceleration in freefall has a value equal to the strength of gravity and so is 10ms-2 on Earth \newline -Weight and gravity force have the same 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}{Forces}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{-forces can be a push, pull, twist, or turn.} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{-forces are measured in Newtons (N)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{-when the forces on an object are unbalanced, that object moves} \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{-only comment/draw uneven forces unless told otherwise} \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{-always have arrows pointing away from the object} \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{-always have arrows touching the object} \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{the forces are {\bf{thrust, friction, gravity, }}and{\bf{ air resistance }}or{\bf{ support}}} \tn 
% Row Count 10 (+ 2)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{balanced forces}} mean the object is stationary or travelling at constant speed} \tn 
% Row Count 12 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{unbalanced forces}} mean the object will either speed up, slow down, or change direction} \tn 
% Row Count 14 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.14011 cm} x{2.83689 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Energy}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{is measured in Joules, J}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-{\bf{Kinetic Energy}} is the energy possessed by a moving object} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{-the more mass the object obtains and the faster it moves, the more kinetic energy it has} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-{\bf{Ek=1/2mv\textasciicircum{}2}}} \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{-{\bf{Gravitational Potential Energy}} is the energy stored in an object because it has been raised a certain height above the ground against the force of gravity} \tn 
% Row Count 10 (+ 4)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{-{\bf{Ep=mgh}}} \tn 
% Row Count 11 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Types of Energy}}} \tn 
% Row Count 12 (+ 1)
% Row 7
\SetRowColor{white}
{\emph{non-stored energy:}} & {\emph{stored/potential energy:}} \tn 
% Row Count 14 (+ 2)
% Row 8
\SetRowColor{LightBackground}
- light and sound & -gravitational (height) \tn 
% Row Count 16 (+ 2)
% Row 9
\SetRowColor{white}
-kinetic (movement) & -elastic (spring) \tn 
% Row Count 18 (+ 2)
% Row 10
\SetRowColor{LightBackground}
-heat & -nuclear (atoms) \tn 
% Row Count 19 (+ 1)
% Row 11
\SetRowColor{white}
-electrical & -chemical (batteries) \tn 
% Row Count 20 (+ 1)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Conservation of Energy}}} \tn 
% Row Count 21 (+ 1)
% Row 13
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\emph{energy is neither created nor destroyed, it is only transferred from one state to another}}} \tn 
% Row Count 23 (+ 2)
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{when energy is converted from one form to another, a proportion is lost as heat and sound energy due to the force of friction} \tn 
% Row Count 26 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}