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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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Dimensionally inconsistent!

This equation doesn't seem to be correct. Dimensionally inconsistent, in fact! How then, is it established? $$s_{t}=v_{0}+\frac{1}{2}a(2t-1)$$ (In case you don't know, this is the equation used to ...
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1answer
40 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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4answers
71 views

Dimensional analysis with derivatives, logs, exponents and trigonometric functions

How should we do dimensional analysis when we have derivatives, logs, exponents and trigonometric functions in an equation. Should we assume that the operands are pure dimensionless numbers? Coming ...
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46 views

Existence of interacting scalar field theory

I saw a comment in Schwartz's introductory text on Quantum Field Theory (cf. Section 14.5) that it is known that $\phi^4$ theory in five dimensions does not exist. In four dimensions it is not known, ...
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What is the unit of transverse speed? [on hold]

$y(x,t)= 2 \sin (3x-3t)$ When I solve using derivation $$\frac{dx}{dt} = 3/3 = \mathrm{Velocity} = 1$$ $$2\times\sin (1)=2\times(0.017)=0.0349$$ 0.0349 m/s OR 0.0349° ?? Please let me know.
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51 views

Can you explain the meaning of base units behind the unit gray?

The gray is a unit that measures energy absorbed per unit of mass. It's defined as one Joule per one kilogram. Which can be simplified to $m^2/s^2$. Can you explain the meaning (interpretation) of ...
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2answers
56 views

Would setting the ideal gas constant to $1$ yield an attractive natural temperature scale? [on hold]

In this recent question, there was a comment 'The "zero point" of Kelvin is natural, but the scale is not'. This led me to wonder whether setting $R = 1$ in the ideal gas law would be an attractive ...
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1answer
83 views

How to calculate fractal dimension by fitting on a log-log plot?

I have simulated a DLA pattern by MC method and the data is for fractal dimension. The right column is the number of particle N(r) into radius r and the left column is the radius r. I plotted a log-...
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12 views

Units of the Klein-Gordon Propagator in SI Units

What are the SI units of the momentum-space propagator of the Klein-Gordon equation for a free particle?
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1answer
38 views

Why is angles given at the end of fundamental units? [on hold]

In my study material, there is a chart of the fundamental units. In that solid angle and angle are separated by a line from the other fundamental units. What is the reason for that?
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7 views

About irrelevance in dimensions & about absorptive and spectral absorptive power

I have read that spectral absorptive power(a) is a dimension less term and total absorptive power(a) is just a ratio hence it is also dimension less. But I have also seen expression in many books that ...
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1answer
102 views

Is there a physical observable with the same units as $c/G$?

Dividing the speed of light $c$ by the gravitational constant $G$ yields the dimension mass*time/area or mass/(length * speed) Is there a physical quantity used in textbooks with this dimension? I ...
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18 views

What Dimensionality Reduction method I can follow on a dataset that has Physics Parameter?

I am trying to model data related to Locomotive Train. We have a various set of parameters and we have the possibility to generate a few more parameters from this. Our model is currently using a lot ...
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1answer
76 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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1answer
41 views

Problem in the continuum limit of a Kronecker delta

I am having troubles in understanding how to correctly perform the continuum limit of a double sum containing a Kronecker delta. Imagine to integrate a function depending on $t$ and $t'$, both ...
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1answer
69 views

What is the dimension of the weak gauge field couplin constant NOT in natural units?

What is the dimension of g and g', NOT in natural units, but in terms of mass, length, time, and permittivity?
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2answers
104 views

Why does electrical resistivity have units of $\Omega \cdot \mathrm{m}$ rather than $\Omega \cdot \mathrm{m}^3 ?$

Electrical resistivity has units of $\Omega \cdot \mathrm{m} .$ However, since resistivity can be described as the resistance of a unit cube, shouldn't the units therefore be $\Omega \cdot \mathrm{m}^...
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1answer
70 views

What are the units of dark energy?

Popular literature seems to equate dark energy with the cosmological constant of the Einstein field equations. We know however that the dimensions of any constituent of the field equations is ${\rm ...
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1answer
48 views

Why can we multiply different units but not add them? [duplicate]

Like units can be added together or, subtracted from one another. However, multiplication and division of units does not have such boundations. multiplication is just repeated addition, similarly ...
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1answer
56 views

Why does the universe manifest scale?

I'll try outline my question in clear terms, articulating specific aspects that are its primary motivators. I'm just beginning in my exploration of physics as a student, but a persistent question that ...
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1answer
65 views

Size of a raindrop

Thinking about the fact that raindrops come with a typical size I was wondering how this can be determined. I am pretty sure that the friction with air and the quantity of water in the clouds are ...
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0answers
52 views

What's does square root of number of atoms mean?

Number of atoms $N$ was counted in 3 dimension. $x,y,z$. However, when calculate it, i.e. in many cases such as refractive index , people take the square root of it, i.e. in reflective index $n=\sqrt{...
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25 views

How to introduce dimensionality in a dimensionless framework?

This question is an extension of this one. I have been told that to introduce dimensionality in a dimensionless quantity I need to multiply with suitable parameters. For instance, for velocity I have ...
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2answers
83 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
57 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
21 views

How to deal with motion on a 2-D lattice in terms of dimension?

I am reading a paper titled: Random walks of molecular motors arising from diffusional encounters with immobilized filaments. There the authors consider the molecular motor moving on a 1-D protein ...
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3answers
142 views

Why does $\sqrt{\frac km}$ represent angular velocity and not frequency?

When I break down $\omega = \sqrt{\frac km}$ (angular velocity for a simple harmonic oscillator) into its units, I get: $$\omega = \sqrt{\frac{kg * \frac {m}{s^2}}{kg *m}}$$ which simplifies to: $$\...
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1answer
32 views

Is cross-sectional area over length classified separately from length?

The ratio of cross-sectional area to length (or its reciprocal) appears in several formulas, including those for electrical resistance and capacitance in terms of the resistivity and permittivity. ...
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4answers
106 views

Do smaller aircraft have lower take-off speeds?

Assuming there are two aircraft, each of the same density and each the same shape, am I correct in understanding that the smaller aircraft would have a lower take-off speed? I have explained how I ...
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2answers
91 views

Are $2$ and $1/2$ universal constants? [closed]

For example, if the equation for energy were: $$E = mc^{2.713397972993}$$ clearly $2.713397972993$ would be a universal constant. And in the Einstein field equation: $$R_{\mu \nu} - \tfrac{1}{2}R \...
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1answer
60 views

Are constants derived or calculated?

I am currently writing up a lab report on the determination of Planck's constant using x-ray diffraction and atomic spectra. In my introduction, I am talking about the history of Planck's constant, ...
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2answers
57 views

Why the quantities are dimensionless in curves plots?

In a lot of plots they use dimensionless quantities, why really we don't let quantities in their physical dimension and plot the curves normally.
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1answer
117 views

Why are angular velocity and angular frequency not measured in Hertz?

Recently, I was doing my homework and I found out that Angular Velocity and Angular Frequency can be calculated using $\omega=v/r$. This means the units of angular velocity and angular frequency are (...
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1answer
61 views

In the SHM equation $F= -kx$, $k =mw^2$ why not use $mf^2$ where $f$ is frequency $w$ here comes out to be $1/s$ not $\text{rad}/s$?

The reason I am stating this is because on calculating the units of w(omega) I found is equal to s^-1 not regular the rad/s. Proof: ...
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3answers
123 views

Do scalar quantities have magnitude only?

I've heard that vector quantities have both magnitude and direction but I've never heard that scalar quantities have magnitude only. Magnitude of vector quantities cannot be negative but what about ...
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1answer
60 views

Why do the units in the period of a mass-spring SHM not work out? [closed]

I am a high school physics teacher having students use the period of a mass-spring system with a known mass to determine the spring constant. We are practicing linearizing functions, so rather than ...
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1answer
23 views

Is (velocity=angular rotation*radius) dimensionally homogenous? [duplicate]

I have been driving myself mad trying to prove it one way or the other, I understand how it is derived and how to use it etc. but it still seems to me to be saying that (m/s)=(rad/s)*(m) which I don't ...
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1answer
33 views

Why is contact resistance measured in $\Omega~\mu m$?

In many papers the contact resistance of a metal in contact with a semiconductor is given in units of $\Omega~\mu m$, for example in the paper by Li et al. (Appl. Phys. Lett. 102 (2013), p. 183110): ...
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1answer
90 views

What makes a system of units self-consistent?

What are the rules governing the creation of a self-consistent system of units? To be clear, I'm not asking about making units universal or replicable, I'm asking about the mathematics governing what ...
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1answer
148 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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1answer
40 views

Notation for feet and inches dimension

I am looking at a set of construction plans where all the dimensions read as x' - y". One example would be 4' - 6". I am confused by the dash in between the feet and inches. Is this supposed to mean ...
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2answers
71 views

Super confused over simple unit conversion from centimeters to cubic centimeters

I'm stuck in a really stupid question. It seems like the meaning of "centi" is chancing meaning. Because if: $ r = 5 cm = 5 \cdot 10^{-2} m $ so $c = 10^{-2}$ But say i need to take the cubic root ...
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4answers
198 views

Is the fine-structure constant related to the size of the observable universe?

The fine-structure constant $\alpha \approx 1/137$. In Planck units, this is also the charge of the electron squared, $e^2 = \alpha$ ($e \approx 0.085$). In Planck units the size of the observable ...
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4answers
236 views

How does natural unit make sense? [duplicate]

Both the fundamental constants $\hbar$ and $c$ have dimensions. In particular, $[\hbar]=ML^2T^{-1}$ and $[c]=LT^{-1}$. But in natural units, we make them dimensionless constants of equal magnitude. ...
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2answers
61 views

About the dimension of the SI units vector space

We know that the set of fundamental and derived physical units can be structured as a vector space over the rational numbers. In the International System of Units the dimension of this space is $7$ ( ...
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2answers
61 views

When is the order of magnitude not equal to the exponent of scientific notation?

Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
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1answer
111 views

When do you use Quantum Mechanics? [duplicate]

Given a problem, how does one know whether to use quantum mechanics or classical mechanics? Take for example electron scattering from a nucleus. The electrons are given a wavefunction in this case. ...
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3answers
157 views

Where is the line between Quantum and Relativity?

Its often said QM is for the very small and GR for the very large. This brings to mind that there should be some limit at which one starts to apply and the other stops. Now I know there are more ...
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2answers
81 views

Dimensions of mass in terms of Length and Time

From Maxwell's Treaties on Electricity and Magnetism: For acceleration due to attraction of a mass m at a distance r is by the Newtonian Law m/(r^2). Suppose this attraction to act fro a very small ...
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1answer
86 views

Hydrodynamic interaction between two spheres in $Re\ll 1$ flow

I am studying the interaction between two spherical particles of radius $a$ in a low Reynolds number flow. Because of linearity, I know that their respective velocities will be linear in the forces ...