>[!summary] Dimensional analysis is a way of determining the dimensions of quantities >[!info]+ Read Time ⏱ **2 mins** # Definition Dimensional analysis is a way of justifying, deriving or proving an equation from the justification of the units (dimensions) of the quantities involved. We denote the dimension of an amount by the []. This table is always true to determine the dimension of a quantity | Quantity | SI units | Dimension Symbol | | ------------------- | ------------- | ---------------- | | Length | Meter (m) | [L] | | Mass | Kilogram (kg) | [M] | | Time | Second (s) | [T] | | Electric Current | Ampere (A) | [I] | | Tempature | Kelvin (K) | [Θ] | | Amount of substance | Mole (mol) | [S] | | Luminous Intensity | Candela (cd) | [J] | ## Examples >[!example] Dimensions of Acceleration From logical definition we know acceleration is the distance over time squared. > >$a = \frac{d}{t^2} = \frac{[d]}{[t]^2}$ Distance is the quantity of length, while time is the quantity of time therefore: > >$ \frac{[d]}{[t]^2} = \frac{L}{T^2} = LT^{-2} >$ --- >[!example] Dimensions of Newtons Second Law By [[Newton Laws|newton's second law]] $\Rightarrow F = ma$ > >$ [F] = [m][a] = [m] [\frac{d}{t^2}] = [M]\frac{[L]}{[T]^2} >$ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/8XrAvR3nn6I?si=xl1ABcuvKWJbTBEE" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! ---