# 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 valid for integrals

Can we apply dimensional analysis for variables inside integrals? Ex: if we have integral $$\int \frac{\text{d}x}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{-1} \left(\frac{a}{x}\right),$$ the LHS has no ...
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### Converting GPa and TPa to N/m

I have a problem with converting units, in some papers, ultimate tensile strength has been shown with GPa or TPa, but in some papers, it has been presented with N/m. (not newton per square meter) As ...
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### Mass Dimension of derivative in a Lagrangian

What is the mass dimension of the derivative $\partial$ in a Lagrangian? I am really confused about this. I read somewhere it is 1 and another place I saw it is -1. Please could someone clear this ...
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### Stokes's law proportionality to radius

Is there a logical explanation why Stokes's drag $F_d=6\pi R \eta v$ is proportional to the radius, $R$ of the sphere? Naively I would have expected that it is proportional to the cross section, i....
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### Are the 7 fundamental SI units able to differentiate between all elementary particles?

More specifically, can the 7 base SI units express qualities like quark strangeness (of quarks) and quark color? How do these SI units differentiate between different quarks (charm, up, top...)?
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### Dimensions of a distance time relation

Recently I came accross a question which was:- Suppose the velocity of a moving particle varies with time as $$v=50t^2.$$ And we have to find out the acceleration at $t = 10s.$ I know that I can use ...
136 views

### Reformulate quantum harmonic oscillator Schrödinger equation using dimensionless quantities

I am trying to rewrite a Schrödinger equation using dimensionless quantities but here, the potential is perturbed by $\lambda x^4$: V(x) = \frac{m\omega^2}{2}x^2 + \lambda x^4\end{...
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### Can the logarithm quotient rule be used when numerator and denominator both have units?

Consider the example of trying to estimate exponential growth rate $\gamma$ from some series of measurements with units vs. time $y(t)$ using the model $y = y_0 \exp{(\gamma t)}$. Solving the model ...
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### Is the seconds cancel out in equation? [closed]

Do the seconds cancel out in this equation leaving seconds instead of seconds squared?
I'm studying Calculus, not physics, but was curious how units work when we consider curl over a 2D velocity field. Given $\mathbf{F} = M(x,y)\mathbf{i} + N(x,y)\mathbf{j}$ the curl is defined to be $(\... 0answers 69 views ### What is the meaning of doing dimensional analysis in Condensed Matter physics? In QFT, we do dimensional analysis because the superficial degree of divergence is related to the dimension of the dimension of coupling constant, but in Condensed Matter physics, the aim of ... 1answer 58 views ### Show that for some$f$it holds that$\dot{\gamma}_0 = \dfrac{U^2\rho}{\eta}f\bigg(\dfrac{Ux\rho}{\eta}\bigg)$I'm not a physicist and I'm having some trouble understanding the following problem: We model the ground by a horizontal flat plate (standing still) with the air or water flowing over it, assuming ... 2answers 90 views ### Problem related to dimensional analysis [closed] In dimensional analysis, why is$\pi$not considered a base quantity (length)? Why is it considered a magnitude? 2answers 117 views ### Is there a natural scale associated with polynomials? This question is related to a previous question asked here. Power laws are scale invariant. They don't have a built-in or characteristic scale associated with them. Exponentials such as$e^{-x/\xi}$... 0answers 148 views ### What are the units of a scalar field if I only impose$c=1$? I know that a scalar field in 4d in natural units ($\hbar = c =1$) has mass dimension 1. We can see this by requiring that the kinetic term in the action $$\int \text{d}x^4 \: \partial_{\mu} \phi \: \... 0answers 29 views ### Can I morph dimensionful physical constants meaningfully? [duplicate] Discussions in the literature (e.g. https://arxiv.org/pdf/1412.2040.pdf) say in no uncertain terms that it is meaningless to consider time variations of fundamental dimensionful parameters such as c, ... 1answer 147 views ### Sciama's paper, On the origin of inertia In his paper "On the origin of inertia", Sciama identifies \frac{\Phi + \phi}{c^2} = -\frac{1}{G} This identity has confused me because I wonder how the right hand side arises since \frac{\phi}{c^... 1answer 66 views ### Given a Force F in newtons, what are the appropriate units for a scalar Q so that F = Q \times 2.00\rm \:N = 20.0\:N? [closed] If:$$ \mathrm{force} = Q \times 2.00\rm \:N = 20.0\:N$$then what does Q equal? What are the appropriate units for Q so the value of the force comes out with the correct units of newtons? 0answers 126 views ### Time rescaling in overdamped Langevin simulation I'm simulating a system according to the Langevin equation (with inertia), however my friction coefficient is high enough that I am essentially in the overdamped regime on the timescales of one ... 2answers 81 views ### Dimensional analysis: a particular problem I don't know how to solve [closed] I have the following configuration: in which a viscous fluid with dynamical viscosity \mu and density \rho slides down the inclined plane due to gravity g. After having solved the Navier-... 2answers 599 views ### Complete list of fundamental properties [closed] What are all of the fundamental properties, that is all measurable quantities which are not derived from anything else? Many quantities are derived e.g. area is length squared, velocity is length per ... 3answers 82 views ### Is energy always measured in units of mass × length^2/time^2 in physics? Is it always M\,L^2/T^2? Is special relativity different from general relativity regarding the units of energy? 5answers 657 views ### 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 ... 1answer 100 views ### Units of the metric tensor or how to get the unit right for the line element In this answer it is stated that the metric tensor elements have no physical unit, i.e. [g_{\mu\nu}] = 1. What is the convention to get the physical unit of the line element ds = g_{\mu\nu}dx^\mu ... 1answer 66 views ### What are the mass dimensions of doublets and singlets? Within the Standard Model (SM) each Lagrangian term has to have a mass dimension of [L] =4. While the mass dimensions of scalar fields [\Phi] = 1, Dirac fields [\Psi] =3/2 and Vector fields A_{\... 1answer 109 views ### The Gauss's law for gravitational field and the unit system Here g is the gravitational field, G is the gravitational constant, and M is the total mass in the volume V. I wonder if this formula holds for any unit system. That is, does the coefficient ... 2answers 180 views ### Definition of stress-energy tensor The image from the wiki article on the stress energy tensor gives T_{00} as 1/c^2 times the energy density. I believe this is incorrect and that the 1/c^2 factor should be dropped. Am I ... 1answer 135 views ### Is frequency\times(time period) = 1 unit? In my book, I have read that the frequency of sound is inversely proportional to the time period i.e., 1/T = \nu. So does that mean$$\text{frequency} \times \text{time period} =1$$i.e., is \nu \... 3answers 114 views ### Dimensionless consistency and quantities I am a chemical engineering student learning about dimensionless quantities. This is a practice question that I am trying. The Van der Waals equation of state can be used to predict the behaviour ... 2answers 104 views ### How does the gradient affect units in physics? I intuitively understand the gradient in a mathematical sense, especially the fact that it points in the direction of maximum increase and easily tells us the function's sensitivity to change in each ... 2answers 130 views ### Minimal substitution, four-potential and units When we make the minimal substitution \begin{equation*} p^\mu\rightarrow p^\mu+\frac{e}{c}A^\mu \end{equation*} the four-potential A^\mu must be proportional to 1/e in order to ensure the whole ... 1answer 83 views ### Why is meters/second the same as meters per second? [closed] In quantities such as speed where the derived (SI) unit is m/s, why do we pronounce it and interpret it as meters per second? My guess is that 1 m is associated with 1 second. Similarly, 5 m/s is ... 1answer 70 views ### Dimensionality Dilemma: Dimensional Analysis Invalidates my Mathematical Model I am trying to derive an equation that describes the rotational motion of an "auto-unravelling system": systems comprised of a material (string, chain, cloth etc.) wound around a cylinder and left to ... 1answer 262 views ### What's the matter with Planck mass M_P in Einstein-Hilbert action? The Einstein-Hilbert (EH) action is often written as$$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}.$$Comparing (1) and (2), one ... 1answer 110 views ### How to convert a quantity in natural units Suppose I am working with a system of units where c = G = \hbar = 1. I can then write e.g. a distance in units of kg by converting with a factor of$$ \frac{c^2}{G} $$Now if I have an energy in ... 1answer 195 views ### Why is k taken as 1 in the derivation of F=kma? [duplicate] In the derivation of F=ma, when we reach the point F=kma, we take k=1. Why can't we take 'k' as some other value? 2answers 85 views ### What allows us to treat physical units in algebra? I have been thinking about this problem:$$Speed = \frac{Distance}{Time}$$Following this, is makes sense that the units of speed is m/s. However, I do not follow why we are able to divide units to ... 1answer 233 views ### Are ‘fundamental measures’ a thing? The question I want to ask is: What measures are needed to describe the physical world and what are the fundamental ones of those, in the proper sense of the word fundamental? But that might be too ... 1answer 88 views ### Why is E=\frac{nh} {2\pi} equal to the energy in the citation below, if h has the dimension of an action? In this article on matrix mechanics in quantum theory you can read, in the subsection of the harmonic osscilator, that$$E=\frac{nh}{2\pi},$$Where$E$stands for the possible energies of the ... 1answer 95 views ### Why dimensional analysis is never off by more that$(2\pi)^{(\pm1)}$? I've been reading about dimensions analysis and at one point it mentions that there could be constants that dimensional analysis fails to define and dimensional analysis is never off by more that$(2\...
What is difference between $\frac{Pa·s}{m}$ and $\frac{Pa·s}{m^2}$? What does that "$2$" after "$m$" mean? I saw both versions,and I dont know if they are same thing or not,no idea what that $2$ is ...