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% Packages
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%\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
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% Document Info
\author{MostAncientDream}
\pdfinfo{
  /Title (alvl-p2-circular-motion-ch10.pdf)
  /Creator (Cheatography)
  /Author (MostAncientDream)
  /Subject (Alvl P2: circular motion (ch10) Cheat Sheet)
}

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% This two commands together give roughly
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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
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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Alvl P2: circular motion (ch10) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{MostAncientDream} via \textcolor{DarkBackground}{\uline{cheatography.com/168994/cs/42363/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}MostAncientDream \\
  \uline{cheatography.com/mostancientdream} \\
  \end{tabulary}
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\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 11th February, 2024.\\
   Updated 11th February, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  Measure your website readability!\\
  www.readability-score.com
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\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*}{2}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{circular motion}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{a force moving in a circular experiences a centripetal force that acts towards the direction {\bf{of axis of rotation}} \newline % Row Count 3 (+ 3)
F = mv\textasciicircum{}2\textasciicircum{}/r \newline % Row Count 4 (+ 1)
velocity is a tangent to the force at a point \newline % Row Count 5 (+ 1)
- constant speed but always changing directions  \newline % Row Count 6 (+ 1)
- therefore there is a variable acceleration% Row Count 7 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{angular velocity}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{w = angular velocity/frequency/speed  \newline % Row Count 1 (+ 1)
in rads\textasciicircum{}-1\textasciicircum{} \newline % Row Count 2 (+ 1)
v = (2pi/T)r = (2pi f)r  \newline % Row Count 3 (+ 1)
therfore  \newline % Row Count 4 (+ 1)
v = wr% Row Count 5 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{loops}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{for vertical loops: \newline % Row Count 1 (+ 1)
you have a circle \newline % Row Count 2 (+ 1)
A- left furthest side \newline % Row Count 3 (+ 1)
B- highest point \newline % Row Count 4 (+ 1)
C- right furthest side \newline % Row Count 5 (+ 1)
D- bottom \newline % Row Count 6 (+ 1)
when travelling-  \newline % Row Count 7 (+ 1)
at A/C \textgreater{} support force = mv\textasciicircum{}2\textasciicircum{}/r \newline % Row Count 8 (+ 1)
B \textgreater{} mv\textasciicircum{}2\textasciicircum{}/r - mg \newline % Row Count 9 (+ 1)
D \textgreater{} mv\textasciicircum{}2\textasciicircum{}/r + mg \newline % Row Count 10 (+ 1)
banked planes/banded tracks: \newline % Row Count 11 (+ 1)
mv\textasciicircum{}2\textasciicircum{}/r = mgtan0  \newline % Row Count 12 (+ 1)
to try and visualise-  \newline % Row Count 13 (+ 1)
-plane coming towards you  \newline % Row Count 14 (+ 1)
-angled towards the left the the right wing face towards the sky \newline % Row Count 16 (+ 2)
-there is mg downwards \newline % Row Count 17 (+ 1)
-centripetal to the left (axis of rotation) \newline % Row Count 18 (+ 1)
- there is a force u angled up the the diagonal left at 0 degrees to the normal% Row Count 20 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}