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\author{anna\_k16}
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  /Title (physics-units-and-dimensions.pdf)
  /Creator (Cheatography)
  /Author (anna\_k16)
  /Subject (physics units \& dimensions Cheat Sheet)
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{physics units \& dimensions Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{anna\_k16} via \textcolor{DarkBackground}{\uline{cheatography.com/152651/cs/32861/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}anna\_k16 \\
  \uline{cheatography.com/anna-k16} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 8th November, 2022.\\
   Updated 27th June, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{units}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{when measuring any physical quantity we compare it to a standard reference point known as a {\bf{unit}}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 2 (+ 0)
% Row 2
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\mymulticolumn{2}{x{5.377cm}}{i) {\bf{fundamental units}}, these are fundamental or base quantities which are not derived} \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{ii) {\bf{derived units}}, these are the units of other physical quantities and can be expressed as a combination of multiple fundamental units} \tn 
% Row Count 7 (+ 3)
% Row 4
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\mymulticolumn{2}{x{5.377cm}}{(together they are know as the system of units)} \tn 
% Row Count 8 (+ 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}{international system of units}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{CGS system}}- the system where centimeter (L), gram (M), seconds (T)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{FPS system}} {[}british system{]}- the system where foot (L), pound (M), seconds (T)} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{MKS system}}- the system where meter (L), kilogram (M), seconds (T)} \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}{International system of units}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{SI units- it's the present system of units which is internationally accepted for measurement.} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{It has {\bf{seven}} base units which then can be combined with each other to form the derived units} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.65466 cm} x{0.86963 cm} x{1.05271 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{SI units}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{quantity}} & {\bf{name}} & {\bf{symbol}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
length & meter & m \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
mass & \seqsplit{kilogram} & kg \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
time & second & s \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
electric & ampere & A \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
Thermodynamic temperature & kelvin & K \tn 
% Row Count 9 (+ 2)
% Row 6
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Amount of substance & mole & mol \tn 
% Row Count 10 (+ 1)
% Row 7
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Luminous intensity & \seqsplit{candela} & cd \tn 
% Row Count 11 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Dimensions of Physical quantities}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{the dimensions of a physical quantity are the powers (or the exponents) to which the base quantities are raised to represent that quantity} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{square brackets {[} {]} are used to indicate the dimensions} \tn 
% Row Count 5 (+ 2)
% Row 2
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\mymulticolumn{2}{x{5.377cm}}{An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. In other words it can be said that dimensional equations represent the dimensions of a physical quantity in terms of the base quantity} \tn 
% Row Count 11 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{examples}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{Volume - {[}V{]} = {[}M\textasciicircum{}0\textasciicircum{} L\textasciicircum{}3\textasciicircum{} T\textasciicircum{}0\textasciicircum{}{]}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Speed - {[}{\emph{v}}{]} = {[}M\textasciicircum{}0\textasciicircum{} L T\textasciicircum{}-1\textasciicircum{}{]}} \tn 
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% Row 2
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\mymulticolumn{2}{x{5.377cm}}{Force - {[}F{]} = {[}M L T\textasciicircum{}-2\textasciicircum{}{]}} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Mass density - {[}{\emph{p}}{]} = {[}M L\textasciicircum{}-3\textasciicircum{} T\textasciicircum{}0\textasciicircum{}{]}} \tn 
% Row Count 4 (+ 1)
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{dimensional analysis}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Dimensional analysis is the practice of checking relations between physical quantities by identifying the dimensions of the physical quantities. These dimensions are independent of the numerical multiples and constants} \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{It helps us deduce certain relations between different physical quantities and checking the derivation, accuracy and dimensional consistency of the mathematical expressions} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{applications of dimensional analysis}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{We make use of dimensional analysis for three prominent reasons:} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{1) To check the consistency of a dimensional equation} \tn 
% Row Count 4 (+ 2)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{2) To derive the relation between physical quantities in physical phenomena} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{3) To change units from one system to another} \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{links for more}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://byjus.com/jee/units-and-dimensions/"\}\}unites and dimension basic pointers\{\{/link\}\}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://byjus.com/physics/dimensional-analysis/"\}\}dimensional analysis (specific)\{\{/link\}\}} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://byjus.com/jee/units-and-measurements-class-11-notes-for-jee/"\}\}notes for the entire chapter\{\{/link\}\}} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://www.examfear.com/notes/Class-11/Physics/Units-and-Measurements/749/Dimensional-Analysis.htm"\}\}more notes for the chapter\{\{/link\}\}} \tn 
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% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://byjus.com/physics/dimensional-analysis-questions/"\}\} questions\{\{/link\}\}} \tn 
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% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://avanti.in/wp-content/uploads/2017/06/Physics\_Module\_Sample\_Class-11.pdf"\}\}pdf of questions\{\{/link\}\}} \tn 
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% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{link="https://dhananjayparkar.wordpress.com/portfolio/dimension-analysis-questions-and-answers/"\}\}HOTS questions\{\{/link\}\}} \tn 
% Row Count 18 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{limitations of dimensional analysis}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Some limitations of dimensional analysis are: \newline % Row Count 1 (+ 1)
1) It doesn't give information about the dimensional constant. \newline % Row Count 3 (+ 2)
2) The formula containing trigonometric function, exponential functions, logarithmic function, etc. cannot be derived. \newline % Row Count 6 (+ 3)
3) It gives no information about whether a physical quantity is a scalar or vector.% Row Count 8 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

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