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 do some of the dimensionful physical constants take on the values they do?

so this might have some duplicated inquiry that this question or this question had, and while i think i have some of my own opinion about it, i would like to ask the community here for more opinions. ...
4
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2answers
2k views

What does the Reynolds Number of a flow represent physically?

What does the Reynolds Number of a flow represent physically? I am having trouble understanding the meaning and the utility of the Reynolds number for a certain flow, could someone please tell me how ...
3
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3answers
204 views

Is it possible to change units in order to simplify the value of an exponential?

I have the equation $$F=e^{E_0 i \pi}, $$ where $E_0$ is the time-independent electric field, and $F$ is just some important value I am trying to calculate. Obviously, it would be better if $F=-1$, ...
3
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1answer
58 views

$c^4$ in Einstein field equations

I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $c^4$ in the denominator. the $8{\pi}G$ term can be obtained ...
3
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1answer
42 views

Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
-1
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1answer
119 views

Why are laws of physics always of product forms?

A first observation is that all the extant laws of physics are of product forms. This phenomenon is somewhat intriguing. The question is: why do law of physics always take, instead of a sum of two ...
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3answers
76 views

Units of a discrete Fourier transform

Normally a Fourier transform (FT) of a function of one variable is defined as $$f_k=\int^\infty_{-\infty}f(x)\exp\left(-2\pi i k x\right) dx.$$ This means that $f_k$ gets the units of $f$ times the ...
2
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2answers
412 views

Why is the candela dimension J, not W?

According to the table at the bottom of the Wikipedia page for the candela, the dimension for candelas is J (joules). Why is this not W (watts)? The luminous intensity for light of a particular ...
5
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1answer
131 views

Data requirement to determine proportionality

A common result of theoretical analysis in physics is some sort of relation derived from physical parameters and typically expressed in the form of a non-dimensional parameter. These scale relations ...
3
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1answer
35 views

Deborah Number for harmonic excitation

I think I do not understand well the concept of Deborah number. It is presented in the sources available to me as the ratio between the relaxation time of a fluid and a characteristic time scale of ...
0
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1answer
152 views

Find out the dimension of $\frac{a}{b}$ [closed]

$E=b-\frac{x^2}{at}$ [x=distance,t=time, E=energy] I have tried following but don't know whether I am correct or not $$\frac{x^2}{at}=E$$ $$\frac{L^2}{aT}=ML^2T^{-2}$$ $$a=M^{-1}T^{1}$$ ...
2
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3answers
98 views

Is quantity a dimension? [closed]

We believe that time is a dimension and that $x$,$ y$, $z$ are dimensions in space. Is quantity a dimension like these? And if not, how do we have dimensionless numbers (like $e$, $\pi$ etc.)?
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1answer
65 views

The position of a particle at any time $t$ is given by $S = V0/a [1-e^{-at}]$. What are the dimensions of $a$ and $V_0$?

To find the dimensions of and V0, I must know the dimension of S and e. So I want to know it.
3
votes
1answer
106 views

How to interpret $t^2$? [closed]

I can't think of the meaning of squaring the Time (multiplying it by itself). It makes sense in Mathematics. But how can you figure it out in nature (or physics). As an example, the formula ...
1
vote
3answers
182 views

Apparent dimensional mismatch after taking derivative

Suppose I have a variable $x$ and a constant $a$, each having the dimension of length. That is $[x]=[a]=[L]$ where square brackets denote the dimension of the physical quantity contained within them. ...
11
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4answers
286 views

Why isn't it $E \approx 27.642 \times mc^2$?

Sorry for the strange question, but why is it that many of the most important physical equations don't have ugly numbers (i.e., "arbitrary" irrational factors) to line up both sides? Why can so many ...
0
votes
2answers
141 views

Taking force, mass and length as base units, find the dimensional formula of velocity [closed]

My doubt is that how can force be considered as a base quantity. Is that possible? How can I represent the dimension of velocity using it?
-1
votes
1answer
41 views

Finding dimensional formula

$$y(x,t)=2A\sin(Kx)\cos(\omega t)$$ $A$ and $x$ are in metre, $\omega$ is angular frequency. Then find dimensions of $A$ and $K$. In this equation how can I find the dimension of $K$?
2
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2answers
126 views

Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi ...
10
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3answers
684 views

How can I understand counterintuitive units like $\text{s}^2$?

One of the things I never understood, but was too afraid to ask is this: how should I think of things like $\frac{\text{kg}}{\text{s}^2}$. What exactly is a square second? Square foot makes sense to ...
2
votes
3answers
99 views

What is a proportionality constant? (Planck's constant)

I understand that Planck's constant is essentially the ratio between the energy of a photon and its frequency. There are 2 things that im trying to verify: isn't the number that Planck's constant ...
2
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3answers
66 views

Is dimensional analysis always sufficient to establish equivalence of quantities?

In dealing with the Biot-Savart law, it was argued that $$ q\frac{d\vec{s}}{dt}\equiv Id\vec{s} $$ using the fact that the units are equal. Does this kind of argument always work? It seems too ...
3
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2answers
193 views

Exponential or logarithm of a dimensionful quantity?

I have a unit measure, say, seconds, $s$. Furthermore let's say I have a dimensionful quantity $r$ that is measure in seconds, $s$. What is the unit measure of $e^r$? ($1/r$ is in $Hz$.) My question ...
0
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1answer
69 views

Dimensional analysis

I was recently introduced to dimensional analysis and I wanted good references for learning the ideas behind it and representation of the natural world. I'm a grad student in biology. I don't have ...
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2answers
115 views

Why do we set $x^0 = ct$ instead of $x^0 = t$?

When we deal with Special Relativity and we start considering spacetime instead of space and time each at once, we usually see books saying that we consider a space with four coordinate $x^\alpha$ ...
0
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1answer
87 views

What does really mean by- power of a number or an exponential function is dimensionless? [duplicate]

Is power of only a number or an exponential function is dimensionless? If power of any other thing can also be dimensionless then please explain with examples.
0
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1answer
80 views

Dimensional Analysis to Determine a Formula

The kinetic energy of a particle confined to a spherical region with a uniform internal potential depends on its mass, the radius of the sphere, and the Planck constant. An electron, confined to such ...
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3answers
746 views

What is the meaning of speed of light $c$ in $E=mc^2$?

$E=mc^2$ is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is ...
6
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0answers
145 views

Why dimensionality of the Electric Charge varies with the spacetime dimensions?

The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did ...
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0answers
28 views

Justifying order of magnitude reasoning

So in the context of a set of notes I am reading about acoustics I get to equation (23) in this paper. Basically it comes down to showing that (note the dots above the a's meaning time derivative!) ...
3
votes
4answers
358 views

$P=ρgh$ - intuitive understanding of the equation?

I've come across this equation recently which relates pressure with the product of density, gravitational acceleration and height difference in a medium. I understand that $P = ρgh$ expands to ...
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1answer
52 views

Order of magnitude estimation for some intriguing questions

The physics TA showed us a few examples in which one can estimate many things from first principles and sound logic based and scaling arguments. This led usually to understanding of why some numbers ...
3
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1answer
67 views

How can Planck units be consistent with conflicting dimensions of mass?

I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = ...
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2answers
94 views

What is dimensional units/quantity and dimensional state

First, I am not a native English-speaking student so I am not good at physics definitions in English. I participated in the MIT e-learning course on classical physics. The 1st lesson is about 3 ...
6
votes
2answers
1k views

Square bracket notation for dimensions and units: usage and conventions

One of the most useful tools in dimensional analysis is the use of square brackets around some physical quantity $q$ to denote its dimension as $$[q].$$ However, the precise meaning of this symbol ...
2
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0answers
227 views

What prediction led to the vacuum catastrophe?

The disagreement between predicted and measured energy density of the vacuum is one of the great unsolved problems of science. According to this book the predicted energy density was obtained as ...
3
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4answers
703 views

Definition of Ohm in SI basic units in words

One way Wikipedia defines Ohm is (this is also teached in school): $$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$ They describe this definition in words, too: The ohm is defined as a resistance ...
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7answers
5k views

What justifies dimensional analysis?

Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular ...
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1answer
138 views

Is there a physical quantity which is the reciprocal/multiplicative inverse of time?

Is there a physical quantity which is the reciprocal/multiplicative inverse of time? If time =distance/speed what is speed/distance. Please forgive my ignorance if there is a really simple ...
6
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1answer
606 views

Why can you remove the gravitational constant from a computer game simulation?

I've seen in a few gravity simulation games (ie. bouncing balls) the equation: force = G * m1 * m2 / distance^2 shortened to this by removing the gravitational ...
2
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1answer
92 views

Dimensional Analysis : Thermodynamics

I was coming across some notes online for phase transitions. In one of the places, the author has written the Claussius-Clayperon equation in this form, $$ \frac{d(ln P)}{d(ln T)} = \frac{T\Delta ...
3
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8answers
746 views

Why does Coulomb's constant have units?

I think of Coulomb's constant as a conversion factor (not sure if this is correct). Kind of like how you would do calculations in kg and then times it by the conversion constant to convert your answer ...
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vote
3answers
160 views

What does the decay constant mean?

In my curriculum, the decay constant is "the probability of decay per unit time" To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a ...
0
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2answers
722 views

Does the Lennard-Jones force equation give its answer in Newtons?

I'm trying to do the dimensional analysis of the Lennard-Jones force to work out what units are being used in my MD simulation. The lennard Jones force is given as the negative derivative of the ...
4
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2answers
318 views

Integrating equations with units

I was looking through an old copy of Barron's AP Physics and found this problem relating to impulse which I was initially confused about how to integrate. Example 6.1 During a collision with a ...
3
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0answers
141 views

Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
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4answers
2k views

Temperature in CGS (Gaussian) units

I've been struggling with conversion from Gaussian to SI units for sometime, trying to figure out how derived units in CGS (current, charge etc) relate to the SI units. But I couldn't find any ...
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4answers
170 views

Could velocity be taken as fundamental instead of time?

In physics time and length are taken as fundamental in the SI system and, as it seems, in the thinking of physicists. Could one instead take velocity, with c as its unit, together with length as ...
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1answer
72 views

Surface gravity for a rotating charged black hole

I have that the surface gravity (at the outer event horizon) for a Kerr-Newman black hole is $$ K_+ = \frac{r_+-r_-}{2(r_+^2+(J/M)^2)} = ...
2
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0answers
176 views

Dimensional analysis to estimate order of magnitude of quantities

In the Coursera course From the Big Bang to Dark Energy on several occasions dimensional analysis was used to estimate the scale of quantities. This almost seems like a contradiction in terms to me, ...