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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Dimension of a scalar field from most general Lorentz invariant Lagrangian

Suppose one is trying derive the dimension of a real scalar field $\phi$ starting from the most general form of the Lorentz invariant Lagrangian $$\mathcal{L}=c_0(\partial_\mu\phi)(\partial^\mu\phi)+...
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3answers
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What is the dimensional formula of angular velocity?

I have problem to determine the dimensional formula of angular velocity. My friend said that the dimensional formula of angular velocity is $T^{-1}$. It's come from rad/s, rad is dimensionless, the ...
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1answer
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Reynolds number in a wind tunnel

I would like to understand how to calculate the Reynolds number in the test chamber of a wind tunnel. It is known that the Reynolds number for a pipe is: $$Re = \frac{UL}{\nu}$$ where $U$ is the ...
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Dimensions and physical quantities [on hold]

2-If a distance (d) has units of meters, and a time (t) has units of seconds, does the quantity (t+d) make sense physically? what about the quantity (d/t)? Explain
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The units when calculating Gyroscopic precession rate don't make sense [on hold]

I was doing a problem set for my physics course and I ran into some odd units for calcualting the gryeoscopic precession rate. As it is the angular velocity of the wheel around the axis, it should be ...
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1answer
51 views

Need guidance in manipulating the formula for frequency

I am confused as to how to go about the following question. The question explains that f refers to the frequency of an oscillation, $m$ refers to the mass of an object attached to a spring, $k$ ...
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1answer
54 views

Why do physical dimensions form an abelian group?

The Wikipedia article on dimensional analysis says: the dimensions form an abelian group under multiplication This is used to justify the manipulation of ratios of incommensurable quantities. My ...
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177 views

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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19 views

How should the spring constant of a cord scale with uniform changes in its overall size? (length and diameter)

Stemming from this: if a girl is playing with a paddle ball, and the toy and her are suddenly shrunk to a size 100 times smaller in all three dimensions, how will this change of scale affect the ...
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2answers
80 views

Does the age of the universe depend on the speed of light?

In the Big Bang theory of the universe, does the value of the speed of light enter into the calculation that determines the age of the universe, and if yes, in which way?
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39 views

Basic question about units of velocity and speed of a curve on a smooth manifold

Frederic Schuller says that velocity has units in Hertz in The WE-Heraeus International Winter School on Gravity and Light. He says: \begin{align} [v^a]&=\frac 1 T \\ [g_{ab}]&=L^2 \\ \Big[\...
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2answers
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Units of the Scalar field theory Lagrangian density [closed]

The Lagrangian (with units $J$) connects to the Lagrangian density (with units $J/m^3$) as: $$ L=\iiint_V \mathcal{L}d^3x $$ Let $\mathcal{L}$ be the classical Lagrangian density of the scalar free ...
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1answer
27 views

Is it only valid to approximate using dimensionless parameters?

In physics we usually have to approximate the behaviour of physical systems. It is often said that if the behaviour of a system depends on a certain parameter with units, then it is meaningless to ...
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Drag - Dimensional Analysis / Buckingham $\pi$

I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on. I'm supposed to consider a small sphere experiencing acceleration due to gravity $g$. The ...
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1answer
143 views

Mass dimension and Abelian super-gauge transformation

A vector superfield is defined by postulating an invariance under a linear transformation in the space of vector superfields: $V \longrightarrow V + i\Lambda - i\Lambda^{\dagger}$ where $i\Lambda - ...
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1answer
251 views

What is the difference between physical dimensions and physical quantities?

What is the difference between physical dimensions and physical quantities if the dimension of mass is also mass?
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What does Planck's Length signify about the reality? How do we know that such a length exists? What is the history of its development? [duplicate]

Wikipedia Says - In 1899 Max Planck suggested that there existed some fundamental natural units for length, mass, time and energy.[5][6] These he derived using dimensional analysis, using only the ...
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68 views

What is the Physical Significance of The Coefficients of Angular Momentum Ladder Operators?

For example, in a spin 1 system in a state $|-1\rangle$, lets raise it twice, and the state becomes $2\hbar^2|+1\rangle$, now lets lower it twice, we get $4\hbar^4|-1\rangle$. Keep going and the $\...
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25 views

Dimension of the constant in Born-Infeld nonlinear electrodynamics

As I know, based on the Lagrangian of Born-Infeld electrodynamics, its constant which shows the strength of electromagnetic field should have the dimension of inverse of length, but in some papers I ...
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2answers
56 views

Is separation of variables in the heat equation dimensionally consistent?

This may be a trivial question but is about the statement that the function $U(x,t) $ in the heat equation may be expressed in the form $X(x)\cdot T(t)$. It's that $X$ and $T$ both are functions ...
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1answer
597 views

Dimensional Analysis in Electromagnetism (SI vs Gaussian-cgs)

Looking at Konopinski's formula for conjugate momentum (in the comment after equation 3 of "What the Vector Potential Describes"): $\mathbf{p}= M \mathbf{v} + q\mathbf{A} /c$ it is plain enough that ...
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1answer
47 views

Method of Dimensional analysis: What does “an expression of product type” mean?

I read in the book Concepts of Physics by HC Verma in the section of Limitations of Dimensional analysis that the method of dimensions cannot lead us to the correct expression sometimes if expression ...
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2answers
101 views

Electrostatic in 2D: dimensional analysis

After reading this very interesting post about the electric field and the electric potential of a point charge in 2D and 1D, I've understood that, for the $2D-$case, the following formulas hold: $$ \...
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1answer
47 views

Can a sequence associated with a physical constant lead to natural laws?

I wondered if we know the universal constants (e.g. gravitational constant, etc.) with high enough precision, and try to find a sequence of which it is part of, or a sequence that converges to it, ...
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3answers
122 views

How to find the corrsponding expression after working with natural units $\hbar=c=1$?

If one does long calculations in natural units how does one find the right expression in let's say SI units in the end? I know that natural units make the calculations easier and also help to show ...
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1answer
51 views

How to reintroduce $\hbar$ and $c$ into a formula written in natural units? [duplicate]

I am looking for a way to translate formulas written in natural units into either HLU units or SI units. Seeing the Planck constant and the speed of light would help me understand what is going on. ...
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1answer
56 views

Strange anomaly in the calculation of the cosmological constant

I was trying to calculate the cosmological constant with two different methods proposed on the internet, that are apparently equivalent but they give different results and different dimensional ...
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1answer
35 views

Differences charge quantity and electric charge

First of all,my english is not well,so sorry for reading. As a senior middle school from China mainland,I am teaching physics about electri field.I with my workmates,get a problem now.We can not get a ...
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1answer
150 views

Is there a general algorithm for conversion of units?

I'm not exactly sure where the best place to put this, as it's more of a general question about dimensional analysis. I decided I was tired of having to convert units all of the time, and was not ...
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3answers
270 views

Can a quantity have two units?

We know that Force has unit of newton and torque has unit of newton meter. Then if you define the energy, which has same magnitude of work then, $W=Fx$ has unit of Joule ( $J$ ) (or $Nm$ ) while $W=\...
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2answers
126 views

Is there a name for this dimensionless quantity?

I have an equation with the nondimensional number $\Delta P L / \sigma$. Here $\Delta P$ is a characteristic pressure drop, $L$ is a characterictic length, and $\sigma$ is a characteristic surface ...
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2answers
1k views

Why do we need more power to do a job fast? [closed]

Let's assume we have two identical electric trains. One has a big electric motor (high power) and the other has small motor (low power). Let us assume the electric motors are of the same brand and ...
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2answers
446 views

Units in general relativity

My question is pretty straight-forward: what are the units of the tensors in General Relativity? This should sound easy, but I always studied those in natural units ($c=1$) so I can't figure it out. ...
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2answers
85 views

Does “phase” in physics always have to expressed in radians or degrees?

According to this post What is a phase of a wave and a phase difference? The phase of the wave is the quantity inside the brackets of the sin-function, and it is an angle measured either in degrees ...
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9answers
2k views

What exactly are we doing when we set $c=1$?

I understand the idea of swapping from unit systems, say from $\mathrm{m\ s^{-1}}$ to $\mathrm{km\ s^{-1}}$, but why can we just delete the units altogether? My question is: what exactly are we doing ...
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1answer
127 views

Why coupling constants with negative mass dimensions lead to non-renormalizable theories?

can somebody explain or point to the relating mathematics showing Why coupling constants with negative mass dimensions lead to non-renormalizable theories?
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49 views

Physical quantity of energy and it's dimension in the article

I am reading an article about Permutation glass by Mobolaji Williams and not sure about the unit (value/dimension) of energy on Fig.3. If $k_BT_c$ is measured in Joules, then I am not totally sure ...
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1answer
2k views

Source for Nusselt number correlation for cooling sphere under forced convection

I've been trying to find a Nusselt number correlation for a sphere cooling in a forced gas cross flow where the sphere temperature is much higher than the free stream temperature. I want something ...
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1answer
1k views

Damping coefficient and damping ratio

I am not sure if I understand the term damping coefficient correctly (I am a high-school student). Here's the link for the info that I learned: http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html ...
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2answers
140 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 ...
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5answers
106 views

Units of variable acceleration

If we have a function, which describes, how a displacement in space along a line varies as a function of time: e.g.: $s(t)=vt$, its units are meters because $[v]=\frac{\text{meters}}{\text{seconds}}$ ...
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1answer
88 views

Question about code units and physical units (hydrodynamics simulations)

I'm working on a code that implements smoothed particle hydrodynamics (SPH) method for solving the equations of magnetohydrodynamics (MHD) with self-gravity. In research papers regarding existing ...
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1answer
2k views

Why revolutions (or turns) are dimensionless?

I think that the reason is because one revolution or one turn is equal to $2 \pi$ rad or to $360$ degrees. We can relate rads and degrees to two units of length that cancel each other. rad $= \frac{...
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1answer
119 views

Undoing problems caused by setting $c = 1$ { or “Undoing $c = 1$” }

In the mathematical derivation of equations for physics, and involving wave propagation in particular, the propagation speed at the start of the derivation is often set to one (c = 1). I am working ...
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2answers
192 views

Why is the equation $E=mc^2$?

The equation $E=mc^2$ never made any sense to me. c is a constant (speed of light), therefore c squared is also a constant. We're not specifying any units so surely the equation should be reduced to ...
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1answer
35 views

Dimensions in the logarithmic form of the Arrhenius equation [duplicate]

The logarithmic form of the Arrhenius equation is: $\displaystyle\ln k=\ln A-\frac{E_a}{RT}$ Here $k$ and $A$ have dimensions whereas $\displaystyle\frac{E_a}{RT}$ is dimensionless. In other words, $...
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25 views

Units and measurement

I read on the characteristics of units (i) It should be easily understandable. (ii) It should be changed with change in physical factors. (iii) It should not change with place or time. I want ...
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1answer
56 views

Reference request: Oldest dimensional analysis books with exercises?

Per the title, what are some of the oldest dimensional analysis books out there with unsolved exercises? Maybe there are some hidden gems from a long time ago out there.
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1answer
31 views

How to approach estimating correction size in the BK equation?

I am starting to do work in theoretical physics, and as a test, the professor I am working with asked me to estimate the size of a correction to an approximate solution to the BK equation. I am no ...
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1answer
32 views

What is the unit of the current in a square barrier model?

In Quantum Mechanics textbooks, the equation for a electron tunneling through a barrier is $$-\frac{\hbar ^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi \left( x\right) +U\psi \left(x\right) =E\psi \left( x\right)...