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.

Filter by
Sorted by
Tagged with
3
votes
5answers
759 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 ...
1
vote
1answer
110 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 ...
0
votes
1answer
71 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_{\...
0
votes
1answer
131 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 $...
1
vote
2answers
192 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 ...
0
votes
1answer
156 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 \...
0
votes
3answers
131 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 ...
0
votes
2answers
116 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 ...
1
vote
2answers
138 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 ...
0
votes
1answer
88 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 ...
-1
votes
1answer
74 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 ...
2
votes
1answer
282 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 ...
-1
votes
1answer
115 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 ...
-1
votes
1answer
248 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?
0
votes
2answers
86 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 ...
-1
votes
1answer
249 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 ...
-3
votes
1answer
93 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 ...
0
votes
1answer
96 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\...
0
votes
2answers
48 views

Confusion about airflow resistivity units

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 ...
0
votes
1answer
142 views

Is Planck angular-frequency equal to 1/Planck-time or $2\pi$/Planck-time?

On wikipedia https://en.wikipedia.org/wiki/Planck_units it states that the angular-frequency is equal to the inverse of the planck time. $$ \begin{align} \omega_p=\frac{1}{t_p}=\sqrt{\frac{c^5}{\hbar ...
1
vote
2answers
370 views

Make an equation dimensionless

Suppose the concentration $c(x,y,t)$ inside a reactor evolves the following $$\frac{\partial c}{\partial t}=D\frac{\partial^2 c}{\partial x^2}-kc , $$ where $D$ is the diffusion coefficient and $k$ ...
0
votes
1answer
634 views

Find dimensional formula of $\alpha$ [duplicate]

The power delivered by a force is given by the relation $$P=\frac{\alpha}{\beta}e^{-\beta t},$$ where $t$ is time. Find the dimensional formula for $\alpha$. So, $-\beta t$ doesn't make sense for the ...
0
votes
1answer
50 views

How should I decide which principal units to use in dimensional analysis based on resulting pi's

Consider an unknown equation involving six different variables: period $T$, in seconds velocity $v$, in meters per second pressure difference $\Delta p$, in Pascal length $L$, in meters volume $V$, ...
2
votes
1answer
114 views

Can you simplify dimensional analysis questions before plugging in values?

If I were to solve the equation: $$d=\frac{a^3}{cb^2}$$ and values were given as so: $a=9.7\ \mathrm m$, $b=4.2\ \mathrm s$, and $c=69\ \mathrm{m/s}$. Why would it be wrong for me to use ...
3
votes
3answers
133 views

Is it possible to build a tiny solar system model?

I'm working through a chapter about forces and I was wondering about the definition of gravitational force of which things of mass are brought together. When thinking about the solar-system this "...
0
votes
1answer
339 views

What is the dimension/unit of a spinor?

I am interested in getting the physical units of a spinor for the usual $(1,3)$ Minkowski spacetime. I am getting 2 different answers, using 2 different approaches! On one hand, using the Lagrangian (...
3
votes
3answers
232 views

Path integral kernel dimensions and normalizing factor

I am currently reading Quantum Mechanics and Path Integrals by Feynman and Hibbs. Working on problem 3.1 made me wonder why the 1D free particle kernel: $$ K_0(b,a) = \sqrt\frac{m}{2\pi i \hbar(t_a - ...
-2
votes
1answer
81 views

Rocket Simulation [closed]

I want to plot the movement of the rocket relative to time ($t$) in the triple dimension $(x, y, z)$. I have all the information about the rocket. I simulate the motion of a rocket. Can you help me to ...
0
votes
4answers
115 views

Why we need Watts in electricity if power is done by the Amps?

If: I = V / R And a light bulb needs X amount of electrons flowing per second (I=amps) to create light. Why do we use watts on the first place if all the light bulb cares is the number of ...
0
votes
2answers
6k views

How to convert the electron volt into Velocity unit?

About this question,I found this from the Wikipedia:nuclear fission produces neutrons with a mean energy of 2 MeV (200 TJ/kg, i.e. 20,000 km/s), which qualifies as "fast". For my question, I only knew ...
0
votes
1answer
220 views

Nusselt Number Correlation of long cylinder in axial flow

What is the Nusselt number correlation of long cylinder in axial (forced) laminar flow? Assume gravity does matter. I have seen numerous sources and lists for cylinders in crossflow which is not ...
0
votes
1answer
101 views

Why does the integral for a “generic one-loop snail diagram” in scalar QFT blow up?

I am embarrassed to ask this but I can't figure it out. Say we are in scalar QFT and we have a Feynman diagram like the following (straight from my course notes) Apparently this integral blows up for ...
1
vote
2answers
277 views

Units of 1d Poisson equation seem… strange

I'm looking at a problem about the voltage along a 1D line, and the poisson equation comes up: $$ \nabla^2 V(x) = \frac{d^2 V}{dx^2} = \frac{\rho(x)}{\epsilon_0}$$ but if I look at the units of this ...
0
votes
2answers
149 views

Uncertainty in multivariable logarithm of a physical quantity

I have a problem in analysis of laboratory data, when I have to take the logarithm of a physical quantity. I know that logarithm is a dimensionless quantity. I have to logarithmize the physical ...
12
votes
3answers
720 views

“Dimensional analysis” arguments in quantum field theory

I'm uncomfortable with dimensional analysis arguments made in quantum field theory, particularly those related to renormalization. For example, in section III.2 of Zee's QFT book, it says: Consider ...
1
vote
1answer
169 views

Why is the mass dimension of the covariant derivative 1?

I'm reviewing an exam, and I can't figure this one out. I know the covariant derivative, but I'm not seeing how it necessarily has a mass dimension.
1
vote
1answer
52 views

Approximations in general

In analysis, a statement like $f(x) \ll g(x)$ (as $x\to x_0)$, has a very precise meaning: $$ \lim_{x\to x_0}\dfrac{f(x)}{g(x)}=0. $$ I was wondering, when physicists write $L_1 \ll L_2$, for, say, ...
2
votes
1answer
121 views

Spin Fields in Superstring

The question is the following and it is related to the article of Martinec, Shenker and Friedan, "Conformal invariance, supersymmetry and string theory" (and to many others actually, but just to be ...
0
votes
1answer
483 views

Error analysis involving exponential

Given equation $$E(t)=A \exp(-bt)$$ $A$ and $b$ are constant and $E$ is energy $t$ is time If there is an error of say 1.5 percent In measured value of t What is error in value of energy. How ...
3
votes
1answer
239 views

Why are physical simulations more accurate with floating point numbers “closer to one”?

I've often heard it said that any sort of "dimensional" (involving length, time, mass, charge, etc.) calculation should be put in a dimensionless form for two reasons Getting a value ~ 1e14 when all ...
0
votes
4answers
374 views

Unit of Angular velocity [duplicate]

Why is the angular velocity $\omega$ always written in $rad/sec$? Is there anything wrong if I write it in $degrees/sec$? If no, then why almost all the books have it as $rad/sec$??
0
votes
1answer
194 views

What units for calculating wavenumber of a matter wave?

So I have a problem where I need to calculate the wave number for proton of energy $40~\rm MeV$. I know the formula for wavenumber of a matter wave is $k = \frac{\sqrt{2mE}}{ \hbar}$. But what units ...
1
vote
1answer
421 views

Dimensional analysis with height and time [duplicate]

I'm very new to physic and I'm watching this physic lecture: https://www.youtube.com/watch?v=GtOGurrUPmQ&list=PLyQSN7X0ro203puVhQsmCj9qhlFQ-As8e&index=2 at the 22:05 he talks about ...
6
votes
2answers
380 views

Why do quantum effects of gravity become important at the Planck scale?

The standard heuristic argument for why quantum effects of gravity become important at the Planck scale is to consider the length scales at which both quantum field theory (QFT) and general relativity ...
-2
votes
1answer
419 views

Does second dimension exist? or any other dimension?

Atoms as we know are the structural unit of everything. As i know that atoms are 3D objects, they have length breath and height (they have thickness).Everything is made up of atoms means everything is ...
3
votes
1answer
126 views

Why don't there seem to be any dimensionless fields in nature?

Scalar fields have dimension 1, spinor fields dimension 3/2, and vector bosons like the photon dimension 1. According to the principles of renormalizability (along with others), this restricts the ...
2
votes
5answers
173 views

Do the units of $G/c^4$ make intuitive sense?

In classical Newtonian mechanics, gravity is explained by: $$F=G \frac {Mm} {r^2}$$ Where $F$ is the force due to gravitation, $M$ and $m$ are the masses of the two bodies in question, $r$ is the ...
82
votes
6answers
13k views

Why is it “bad taste” to have a dimensional quantity in the argument of a logarithm or exponential function?

I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although ...
1
vote
1answer
134 views

Can Electric Field and Gravitational Field be added vectorially? [closed]

As both fields follow Superposition Principle, can they be added to get a total field at any region?
1
vote
3answers
141 views

Why the time period cannot depend upon the angular velocity and angular acceleration of the pendulum?

To derive the time period $T$ of a pendulum using dimensional analysis it is assumed that it depends upon the mass $m$ of the bob, the length of the string $\ell$, the acceleration due to gravity $g$ ...