# 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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### Is dimensional analysis wrong?

In many physics textbooks dimensional analysis is introduced as a valid method for deducing physical equations. For instance, it is usually claimed that the period of a pendulum cannot possibly depend ...
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### Dimensionless consistency and quantities

I am a chemical engineering student learning about dimensionless quantities. This is a practice question that I am trying. The Van der Waals equation of state can be used to predict the behaviour ...
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### How does the gradient affect units in physics?

I intuitively understand the gradient in a mathematical sense, especially the fact that it points in the direction of maximum increase and easily tells us the function's sensitivity to change in each ...
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### Minimal substitution, four-potential and units

When we make the minimal substitution \begin{equation*} p^\mu\rightarrow p^\mu+\frac{e}{c}A^\mu \end{equation*} the four-potential $A^\mu$ must be proportional to $1/e$ in order to ensure the whole ...
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### Why is meters/second the same as meters per second? [closed]

In quantities such as speed where the derived (SI) unit is m/s, why do we pronounce it and interpret it as meters per second? My guess is that 1 m is associated with 1 second. Similarly, 5 m/s is ...
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### Dimensionality Dilemma: Dimensional Analysis Invalidates my Mathematical Model

I am trying to derive an equation that describes the rotational motion of an "auto-unravelling system": systems comprised of a material (string, chain, cloth etc.) wound around a cylinder and left to ...
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### What's the matter with Planck mass $M_P$ in Einstein-Hilbert action?

The Einstein-Hilbert (EH) action is often written as $$S_{EH}=\frac{c^4}{16\pi G}\int d^4x \sqrt{-g}R\tag{1}$$ and often as $$S_{EH}=\int d^4x \sqrt{-g}M_P^2 R\tag{2}.$$ Comparing (1) and (2), one ...
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### How to convert a quantity in natural units

Suppose I am working with a system of units where $c = G = \hbar = 1$. I can then write e.g. a distance in units of kg by converting with a factor of $$\frac{c^2}{G}$$ Now if I have an energy in ...
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### Why is $k$ taken as 1 in the derivation of $F=kma$? [duplicate]

In the derivation of F=ma, when we reach the point F=kma, we take k=1. Why can't we take 'k' as some other value?
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### What allows us to treat physical units in algebra?

I have been thinking about this problem: $$Speed = \frac{Distance}{Time}$$ Following this, is makes sense that the units of speed is m/s. However, I do not follow why we are able to divide units to ...
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### Are ‘fundamental measures’ a thing?

The question I want to ask is: What measures are needed to describe the physical world and what are the fundamental ones of those, in the proper sense of the word fundamental? But that might be too ...
### Why is $E=\frac{nh} {2\pi}$ equal to the energy in the citation below, if h has the dimension of an action?
In this article on matrix mechanics in quantum theory you can read, in the subsection of the harmonic osscilator, that $$E=\frac{nh}{2\pi},$$ Where $E$ stands for the possible energies of the ...