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\author{rehman225}
\pdfinfo{
  /Title (physics-units-and-dimensions.pdf)
  /Creator (Cheatography)
  /Author (rehman225)
  /Subject (Physics - Units and dimensions Cheat Sheet)
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\noindent
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    {\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{Physics - Units and dimensions Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{rehman225} via \textcolor{DarkBackground}{\uline{cheatography.com/152970/cs/33031/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}rehman225 \\
  \uline{cheatography.com/rehman225} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 6th July, 2022.\\
   Updated 6th July, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Physical quantity}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Physical Quantity is a quantity that can be measured or can be quantified. \newline % Row Count 2 (+ 2)
{\bf{Examples}} : Mass, Length, Force. \newline % Row Count 3 (+ 1)
Physical quantity can be classified into, \newline % Row Count 4 (+ 1)
1. Fundamental or base quantities. \newline % Row Count 5 (+ 1)
2. Derived Quantities.% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Derived Quantities}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{The physical quantities that depend on other quantities and can be derived from other physical quantities are known as derived quantities.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{The units of derived physical quantities are called as derived units.} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Example}} : Area, Volume, Density etc.} \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4.256 cm} x{1.596 cm} x{1.748 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{S.I System of Units}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Fundamental Quantity}} & {\bf{Unit}} & {\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 4 (+ 1)
% Row 3
\SetRowColor{white}
Time & Second & s \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Electric current & Ampere & A \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
Temperature & Kelvin & k \tn 
% Row Count 7 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Intensity of light & Candela & cd \tn 
% Row Count 8 (+ 1)
% Row 7
\SetRowColor{white}
Quantity of substance & Mole & mol \tn 
% Row Count 9 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{8.4cm}}{{\bf{Supplementery Quantities}}} \tn 
% Row Count 10 (+ 1)
% Row 9
\SetRowColor{white}
Plane angle & Radian & rad \tn 
% Row Count 11 (+ 1)
% Row 10
\SetRowColor{LightBackground}
Solid Angle & \seqsplit{Steradian} & sr \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.204 cm} x{3.42 cm} x{1.976 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Dimensional Formulas List}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Physical Quantity}} & {\bf{Formula}} & {\bf{Dimensional Formula}} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Area (A) & Length x Breadth & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}0\textasciicircum{}{]} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Speed (s) & Distance / Time & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
Velocity (v) & Displacement / Time & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn 
% Row Count 9 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\seqsplit{Acceleration} (a) & Change in velocity / Time & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 11 (+ 2)
% Row 5
\SetRowColor{white}
Linear momentum (p) & Mass x Velocity & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn 
% Row Count 13 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Force (F) & Mass x Acceleration & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 15 (+ 2)
% Row 7
\SetRowColor{white}
Work (W) & Force x Distance & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 17 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Energy (E) & Work & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 19 (+ 2)
% Row 9
\SetRowColor{white}
Impulse (I) & Force x Time & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}1\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn 
% Row Count 21 (+ 2)
% Row 10
\SetRowColor{LightBackground}
Pressure (P) & Force / Area & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}-1\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 23 (+ 2)
% Row 11
\SetRowColor{white}
Power (P) & Work / Time & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-3\textasciicircum{}{]} \tn 
% Row Count 25 (+ 2)
% Row 12
\SetRowColor{LightBackground}
Angular velocity( ω ) & Angle / Time & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn 
% Row Count 27 (+ 2)
% Row 13
\SetRowColor{white}
Angular \seqsplit{acceleration(} α ) & Angular velocity / Time & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 30 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{2.204 cm} x{3.42 cm} x{1.976 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{8.4cm}}{\bf\textcolor{white}{Dimensional Formulas List (cont)}}  \tn
% Row 14
\SetRowColor{LightBackground}
Angular momentum (J) & Moment of inertia x Angular velocity & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-1\textasciicircum{}{]} \tn 
% Row Count 2 (+ 2)
% Row 15
\SetRowColor{white}
Torque (𝞽) & Moment of inertia x Angular acceleration & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 5 (+ 3)
% Row 16
\SetRowColor{LightBackground}
\seqsplit{Temperature} & —— & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}0\textasciicircum{}T\textasciicircum{}0\textasciicircum{}K\textasciicircum{}1\textasciicircum{}{]} \tn 
% Row Count 7 (+ 2)
% Row 17
\SetRowColor{white}
Heat (Q) & Energy & {[}M\textasciicircum{}1\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 9 (+ 2)
% Row 18
\SetRowColor{LightBackground}
Latent heat (L) & Heat / Mass & {[}M\textasciicircum{}0\textasciicircum{}L\textasciicircum{}2\textasciicircum{}T\textasciicircum{}-2\textasciicircum{}{]} \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Fundamental or Base Quantities}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{The physical quantities that do not depend on other quantities and exits independently are known as fundamental or base quantities.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{The units of fundamental quantities are called as fundamental units.} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Example}} : Length, Mass, Time etc.} \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Units}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic standard called unit.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Four main system of representation of units are,} \tn 
% Row Count 4 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{FPS}} - Foot pound second} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{CGS}} - Centimeter gram second} \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{{\bf{MKS}} - Meter kilogram second} \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{SI}} - Internationally system of units.} \tn 
% Row Count 8 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Advantages of SI system}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Coherent system of units i.e., units are derived by the multiplication or division of set of fundamental units.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Rational system of units i.e., uses ine unit for one physical quanity.} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{S.I is a decimal system and makes the calculation work easy.} \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{S.I system is a combination of practical and theoretical work.} \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Dimensions}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{The powers to which the fundamental units are to be raised to obtain one unit of the quantity are termed as dimensions of a physical quantity.} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Dimensional Formula}}} \tn 
% Row Count 4 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{The expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity is termed as dimensional formula of that quantity.} \tn 
% Row Count 8 (+ 4)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Dimensional formula of any quantity can be expressed as {\bf{{[}M\textasciicircum{}a\textasciicircum{}L\textasciicircum{}b\textasciicircum{}T\textasciicircum{}c\textasciicircum{}θ\textasciicircum{}d\textasciicircum{}{]}}}} \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{where,} \tn 
% Row Count 11 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{M - Mass} \tn 
% Row Count 12 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{L - Length} \tn 
% Row Count 13 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{T - Time} \tn 
% Row Count 14 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{θ - Temperature} \tn 
% Row Count 15 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Dimensional Constant}}} \tn 
% Row Count 16 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{The constants having dimensional formulae are called dimensional constants} \tn 
% Row Count 18 (+ 2)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Ex}} : Plank's Constant, universal gravitational constant} \tn 
% Row Count 20 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Homogeneity, Applications and limitations of D.F}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{The physical quantity on the left side of the equations should have the same dimensions as on the right side of the equation} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Application of Dimensional Formula}}} \tn 
% Row Count 4 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{(a) To verify the correctness of the equation.} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{(b) To convert the one system of units to another system.} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{(c) To derive relationship among different physical quantities.} \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{{\bf{Limitations of Dimensional Method}}} \tn 
% Row Count 10 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{(a) The values of dimensionless constants and proportionality constants cannot be determined using dimensional analysis.} \tn 
% Row Count 13 (+ 3)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{(b) This method is not applicable if an equation is sum or difference of two or more quantities.} \tn 
% Row Count 15 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{(c) It is not applicable to the trigonometry, logarithmic and exponential functions.} \tn 
% Row Count 17 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{(d) It cannot be used to find proportionality constants.} \tn 
% Row Count 19 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}