# Tagged Questions

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 the concept of work only defined in mechanics?

I'm studying energy and work, so far it looks like work only makes sense in kinematics (objects that move), but energy makes sense in many other ways (electric, thermodynamic, mechanic). Is work a ...
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### Is “power to mass ratio” in fact independent to mass?

I was trying to find power to mass ratio of sun (work done per second at each unit mass at average), but I found the unit is quite straight: $W=kg \space m^2 s^{-3}$ Then $W/kg= m^2 s^{-3}$ Which ...
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### Non-dimensionalizing incompressible Navier-Stokes

I have a question about non-dimensionalization of the incompressible Navier-Stokes (NS) equations. My understanding is that the purpose of non-dimensionalization is to "collapse" solutions onto one ...
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### Proper units for physical quantities when $\hbar$=$1$

How to deal with the units of quantities if $\hbar=\tfrac{h}{2\pi}=1$? For example, the energy $E=\hbar\omega$: If I have chosen $\hbar=1$, how do I use the units to properly differentiate between ...
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### Dimensional equation for measuring logarithm of volume

I have a measure that uses radiation dose (M.U. $Gray$) and $\log(Volume)$. The measure is $[\frac{Dose}{\log(Volume)}]$ that is $[\frac{D}{\log(l^3)}]$ with $D$ as radiation dose (M.U. unit is Gray) ...
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### Drag - Dimensional Analysis / Buckingham Pi

Dimensional Analysis / Buckingham Pi Theorem I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on for practice. I'm suppose to consider a small ...
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### When can two quantities be added together?

Whenever two things are to be added together, one typically needs to check whether this actually makes sense, and an addition is said to make sense, in principle, when the units match up. Yet, ...
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### Visualizing Physical Units in Phyiscs

I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I ...
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### Connection between the cosmological constant $\Lambda$ and the cutoff scale $\Lambda$

I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT. Cosmology: The cosmological constant enters the Einstein equations. In the special case of the ...
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### Issues of normalization & differential final state momenta in analysis of normalized differential quantum-field-theoretic probability of scattering

The normalized differential quantum-field-theoretic probability $dP$ of scattering is given by $$dP=\frac{|\langle f |S|i\rangle|^{2}}{\langle f|f\rangle\langle i|i\rangle}d\Pi,$$ where $|i\rangle$ ...
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### Dimensional consistency of an equation

We know that if an equation has to be physically correct then it must be dimensionally consistent i.e. If an equation is not dimensionally correct then it can never be physically correct. Now in the ...
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### Books or other sources for natural units, Planck units, dimensional analysis etc. for someone with only high-school physics knowledge

I'd like to know more about natural units, Planck units, dimensional analysis, etc., and things like how units are "created" by man or by the universe, universal constants and where they come from. ...
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### Is the dimension “number of particles” a fundamental, or derived dimension (based on mass), or does it depend on the context, or is it dimensionless?

I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on. "Derived quantities" have dimensions that can be written in terms of ...
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### Dimensional inconsistency in first law of black hole thermodynamics

The first law of black hole mechanics (let's simplify by considering a uncharged and non-rotating black hole) can be written as $$\delta M = T \delta S$$ If I use the definition of Hawking ...
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### Finding the exponent of $\lambda$ in Wien's displacement law

I am reading this paper on a short history of the $T^4$ radiation law. In particular, on page 5, By assuming that the wavelength of radiation emitted by a molecule was a function only of its ...
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### What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
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### Black Hole Entropy Calculation

I was watching "Leonard Susskind on The World As Hologram" ( youtube ). At one point he describes the way Bekenstein calculates the entropy of a black hole. Paraphrasing: Take a minimally sized black ...
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### Non-dimensionalizing the “bead on a rotating hoop, with viscous damping” problem

This is not a homework question. Rather, this is an exercise I have taken up on myself. In particular, I am trying to find an algorithmic way to non-dimensionalize known equations, using the ...
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### Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is scale-...
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