# 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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### Why can't I balance the units in the equation for power of a sound wave?

According to this answer (source), the time averaged power $P$ of an acoustic wave is: $$P = \frac{1}{2} \mu v \omega^2 A^2$$ Where $\mu$ is mass density of the medium, $v$ is speed of sound in the ...
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### Converting Tesla (classical magnetic field unit) to $\rm GeV^2$ (QFT magnetic field unit)

I want to do research on hadrons in a presence of an external magnetic field but I need to know how convert Tesla to $\rm GeV^2$. Can you explain that to me?
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### What's the link between Planck Mass squared and $1/8πG$?

Good morning, In an equation of an article, we said that 1/8πG = Mass of Planck^2. But 1/8πG = 596175243.8, is much larger than the Planck Mass^2 = 1.383*10-16 kg. Is there a conversion to do? If not, ...
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### How can the unit of Newtons measure both gravity and electromagnetism?

For context, I was thinking about forces. Force is the mass of the particle multiplied by the acceleration it undergoes. There are different kinds of forces, for example, gravity and electromagnetism. ...
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### The universal value of Boltzmann constant?

So I'm quite confused about Boltzmann's constant $k_B$ being fundamental. From here: ... the Boltzmann constant. Its value is well known but even if its value were 10 times bigger or if it were ...
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### Is amount of substance fundamentally a scalar quantity? (in the mathematical sense of scalar)

Reading the SI (and ISO) standard for units and quantities, I'm currently puzzled by something very subtle. If I can see and understand why we talk about scalars, vectors, and tensors in the context ...
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Consider, a particle is moving in a harmonic oscillator potential : $V=\frac{1}{2}m\omega^2x^2$. The force on the particle will be : $F=-m\omega^2x$. What is the unit of $\omega$ here ? Is it $Hz$ or ... • 151 0 votes 1 answer 50 views ### Derive the dimensionless Gibbs free energy equation [closed] I'm having trouble deriving the Gibbs free energy equation: $$G = \sum_i n_i \left(g_i^0(T) + RT\ln P_i\right),$$ then, $$\dfrac{G}{RT} = \sum_i n_i\left[\dfrac{g_i^0(T)}{RT} + \ln P + \ln\left(\... • 15 0 votes 0 answers 41 views ### Why the Cauchy Stress Tensor & the Stress-Energy-Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Stress-Energy-Momentum Tensor's units? What math operation(s) (if any) would transform the 3D Cauchy Tensor into the 4D Energy Momentum Tensor of GR? • 1 0 votes 1 answer 86 views ### How does the \beta factor appear in eq. (4.33) of Altland, Simons "Condensed Matter Field Theory"? In Altland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states: however, immediately after that, a beta factor shows ... 1 vote 1 answer 70 views ### Why are we interested in the dimensional analysis/power counting in string theory? I'm learning bosonic strings on my string theory course; here is part of my notes about the dimensional analysis on the world sheet \Sigma and the spacetime manifold \mathcal{M}: I learned this ... • 1,305 1 vote 1 answer 49 views ### Small and large extra dimension(s) of the physical space Trying to make sense of small and large extra dimension(s) of phyiscal space in a simple intuitive example. Consider a two dimensional manifold like \mathbb{R}^2 and we are trying to add a small and ... 0 votes 1 answer 48 views ### When do you use ΔU= mCΔT in thermodynamics? [duplicate] I am confused between when to use ΔU= nCvΔT and ΔU= mCΔT. For example a question says 100g of water is heated from 30°C to 50°C, ignoring the slight expansion of water the change in its internal ... 1 vote 2 answers 103 views ### Why does dimensional analysis work? I need a elementary reason [duplicate] I understand this is a very elementary question, but I haven't been able to come up with any elementary reason why it should work. Also, why should quantities in an exponential be dimensionless? 1 vote 0 answers 21 views ### Looking for dimensional analysis practice [closed] I just finished Bridgman's book on dimensional analysis, and am trying to work through the problems. Does anyone know of an answer key for Bridgman's book? Here is the book in question: https://www.... 0 votes 1 answer 42 views ### Basic question about units in range formula [closed]$$R = \frac {2v_0^2sin \theta cos \theta}{g}velocity is \frac fs and g is \frac {f}{s^2} which would seem to be \frac fs \times \frac {s^2}{f} resulting in s after cancellation, yet the ... • 111 1 vote 0 answers 18 views ### Why aren't the interatomic Heisenberg exchange coupling parameters reported in units of energy/units of spin squared? The Heisenberg Hamiltonian is H_{Heis}=-\sum_{ij} J_{ij} \langle \vec{S}_i \cdot \vec{S}_j \rangle (generally, save different constants depending on convention). This seems to suggest that the ... • 11 1 vote 1 answer 65 views ### Is action an extensive quantity - always? Action, the integral over time of the kinetic minus the potential energy seems to be an extensive quantity. (There is nothing serious coming up in Google on this issue. Neither on Google Scholar.) In ... • 577 0 votes 1 answer 40 views ### Units and dimensions in equations [closed] If I said, for which value of r does a circle have equal area and circumference, we could all calculate that it happens when r=2, but when written out, are we not saying that an area equals a ... 0 votes 2 answers 43 views ### How to compute the Reynolds number of a fluid without knowing the density? I am running a simulation with LAMMPS involving a colloid suspended in a fluid. Simple shear is applied creating flow. My question is, how can I calculate the Reynolds number of the fluid given I don'... 0 votes 1 answer 47 views ### Einstein coefficient unit Einstein-A coefficient of diatomic molecule can be written as (W. A. Brown, 1970): [unit] A= 1/sec (transition probability, Einstein coefficient) h-bar= Joule*Second (planck constant) Re=Coulomb*... 0 votes 1 answer 55 views ### A Problem in Scaling Question: - If the size of the nucleus (in the range of 10^{-15} m to 10^{-11} m ) is scaled up to the tip of a sharp pin, what roughly is the size of an atom? (Assume the tip of the pin to be in ... • 31 4 votes 4 answers 186 views ### ℏ in the canonical commutation relation I am wondering what the physical meaning of the introduction of a "new" constant \hbar in the CCR [\hat{x},\hat{p}]=i\hbar is if you compare it to the classical Poisson-bracket \{x,p\}=... 0 votes 2 answers 73 views ### Unit of v in v=rω [duplicate] unit of velocity is m/sec but in v=rω unit of r is metre and unit of ω is radian/sec so unit of v should be radian*metre/sec but it is m/sec how I know this is dimensionally correct but I dont ... 1 vote 1 answer 85 views ### The Ricci scalar in FRW, where am I getting wrong? I'm trying to derive Ricci scalar with FRW metric, but additional c^2 makes me confused. The book by D. Baumann says \begin{align} R &= g^{\mu\nu}R_{\mu\nu} \\ &= -R_{00}+\frac{1}{a^2}R_{... • 127 0 votes 1 answer 60 views ### Normalized units versus dimensionless units In a molecular dynamics code, suppose, the distances are expressed in units of a characteristic length of the simulated system, R_0. In some papers it is written as, " distances are normalized ... • 151 1 vote 1 answer 38 views ### Dimensional Analysis Does Not Check Out [closed] I'm looking over the lecture notes found here, and if you scroll down to the end of page 2, the writers make the statement A(\omega _d) = \dfrac{f_0}{\sqrt{\omega_0^2 - \omega_d^2 + \omega_d^2\Gamma^... • 617 1 vote 1 answer 97 views ### How do you go from watts to lumens? let's say you have a light source and using a solar panel or photoelectric diode you can absorb all the emitted light, which would produce some amount of power outputted by the solar panel. How would ... 0 votes 1 answer 50 views ### At What Scales Turbulence Matters? So from what I understand(like from this site: https://www.britannica.com/science/transport-phenomenon) is that turbulence is when the flow is almost unpredictable at different parts but on average ... 2 votes 2 answers 94 views ### Electric field and potential of a point charge in a (strictly) 2D 'world' I was trying to figure out how the electric potential and electric field are different in a 3D system versus in a 2D system (I take such a 2D 'world' to be the xy-plane, i.e. z=0, in a Cartesian ... • 21 0 votes 3 answers 69 views ### Why can we only use radians in the arc length formula? [closed] Why can't we use degrees in the arc length formula (S = R\theta)? Why only radians? I don't understand because radians and degrees are both dimensionless. • 41 2 votes 2 answers 32 views ### Question about unit for intensity The picture is from one physics textbook about treating sun as a blackbody and compare the electromagnetic radiation spectrum. Note the unit used for Intensity in the picture shown, it's Watts / (... • 121 2 votes 0 answers 30 views ### Are there any similarities between the Action S and Angular momentum L, since they have they same units? [duplicate] Action is defined as: S = \int_{t_1}^{t_2} L dt,$And has units of joule-second. Angular momentum has the same units, but has a completely different application and interpretation. Are there any ... • 1,316 4 votes 1 answer 107 views ### How to reinvent measurement units? Imagine you're in deserted island. You will eventually need to know how much there is of something or how long is some thing. Is there a way to get all main measurement units (kg, m, °C, m$^3$, etc.) ... • 151 0 votes 2 answers 128 views ### What is the logic behind Planck units? I was curious to know the logic behind “Planck Units”, I read this question but did not understand it. Do you have a better (simpler) explanation for setting$c = G = \hbar = 1$? • 117 1 vote 2 answers 111 views ### Why use units of$\rm 1/Hz$instead of$\rm s$? The Wikipedia page for Planck's constant frequently includes the constant in units$\text{J/Hz}$or$\text{J} \times \text{Hz}^{-1}$. Is there a reason these units are used instead of$\text{J} \times ...
I was watching the first lecture of Special Relativity by Leonerd Susskind (link:Youtube) whereby setting the speed of light to 1, i.e. $c = 1 \dfrac{[l]}{[s]}$, where \$[l] = 3 \cdot 10^8 \dfrac{[m]}{[...