# Questions tagged [dimensional-analysis]

Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

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### What are $δ$ and $ε$ in the list of Dirac's five 'fundamental constants', concerning his 'Large number hypothesis'?

From Jean-Philippe Uzan's Varying Constants, Gravitation and Cosmology: Dirac formed five dimensionless ratios among which1 δ ≡ H0ħ/mpc2 ∼ 2h × 10−42 and equation M1 and asked the question of which of ...
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### Scaling difficulty of landing a rocket

I am wondering whether it is more difficult to land (as spaceX does) a rocket of height $k L$ than landing a rocket of height $L$? Is there some scaling law? Or at least is there a way to see in the ...
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### String length $\gg$ Planck length?

The potential energy of a string $E_{pot}$ is given by $$E_{pot}=T \times L\tag{1}$$ where $T$ is the string tension and $L$ is the length of the string. The internal kinetic energy $E_{kin}$ of a ...
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### Why is $\exp(-1)$ a good benchmark in many physics? [closed]

In many subjects in Physics (not only phys though), we often encounter a value which gives $\exp(-1)$, such as a time constant in circuitry ($\exp(-t/RC)$, $t=RC$ gives $exp(-1)$), lifetime, mean free ...
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### $G$ expressed as a function of $c$?

The escape velocity for a given mass $M$ and a given radius $r$ is given by: $v_e = \sqrt{ \frac{2 G M}{r} }$ With $M$ = 25 kg and $r$ = 1/$c$ we have: $v_e = 1.0001917061 \approx 1$ Can we express $G$...
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### Why is the charge density of a rod in $\rm C/m$ and not in $\rm C/m^2$?

Is it because we consider the rod to be a 1-dimensional straight line? Or is there any other reason? I know it sounds like a stupid question but I am confused in this regard.
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### Under what circumstances can we make sense of functions of dimensionful arguments?

Solving Laplace's equation in 2D assuming symmetry $\theta \rightarrow \theta + \delta \theta$ yields $$\phi(r) = \alpha \log(r) + \beta.$$ This is discomforting because $r$ has dimensions of length; ...
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### Test tank physics

In a test tank scaled-down simulation of, for example, a ship stability problem, is it not incorrect to assume that water will behave in a scaled-down fashion with regard to wave period? Don't we need ...
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### How to check the conformal prefactor in a correlation function?

In CFT it is usual practice to extract the so-called conformal prefactor from the correlators in order to isolate a function which depends only on the cross-ratios. For example the $4$-point function ...
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### Mathematical Reasoning In Physics

Does this form of reasoning have a name. I often see it but am a little confused on how to read/understand it and wanted to look more into it but don't know what to call it Ex. Let's call the force ...
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### Fundamental quantities in physics

I observed that the fundamental units like meter, kilogram, ampere, kelvin and candela are all indirectly dependent on one single fundamental value 'second' and each other. For example: Meter:- 1 ...