Questions tagged [units]

Units are standards of measurement used for different types of quantities.

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How do I determine what physical constants can be combined to derive a set of natural units?

I am looking into natural units (units of measurement based only on universal physical constants). Different systems of natural units use different physical constants as their defining constants. If I ...
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Couldn't understand an example used in explaining fundamental and derived quantities

In my book under topic of fundamental and derived quantities, there is an example which is supposed to explain this concept and it goes like this, As a simple example, if a unit of length is defined, ...
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A bottle weights 4.5kg, what's its mass in TeV (Terra Electronvolts)? [closed]

I'm not entirely sure about this problem. And the second one says: An apple falls down from a height of 1 meter. What's it's kinetic energy? My thoughts: 1/2gt^2= 1 meter -> solve for t, then v=s/t ...
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Scaling factor for the right unit?

I have the following equation in front of me $$ x = \frac{\rm constant}{(1+b_1/K_1)^2 (1+(b_2/K_2)} $$ where "constant" is a dimensionless quantity and $b_1,b_2,K_1,K_2$ are measured in mmol/...
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Magnetic flux from maximum induced emf as a function of angular velocity?

I've done an experiment where I have a small rotating coil in a uniform magnetic field and I've measured the induced emf in the rotating coil as a function of time for several different angular ...
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Conventions Consistency For the Dirac Field

I am writting a text and I try to be consistent with my definitions. I have expanded my fields in modes in the following way $$\psi(x)=\int\frac{d^3\vec{p}}{(2\pi)^3\sqrt{2p^0}}\sum_s\bigg(u_s(\vec{p})...
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Different units of measure for the specific intensity and the components of the Stokes vector

Good morning to all, I'm a bit confused about the fundamental physical quantities adopted in the theory of radiative transfer. In particular, many texts show the scalar integro-differential equation ...
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Why is $(\text{kg} \cdot \text{m}^2)/\text{s}$ written as "Joule second" when there is no joule present, and time is divided and not multiplied?

The Joule is $(\text{kg} \cdot \text{m}^2)/\text{s}^2$, which is not contained in $(\text{kg} \cdot \text{m}^2)/\text{s}$, the Joule second. So, why does the unit name contain "Joule"? Also, ...
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CGS of resistance

What's the CGS unit of resistance? Is it the same as that in SI system, i.e. ohm (Ω)? I googled but found no explicit answer.
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Unit issues with commutator relations with two dependent variables

Suppose I have the following commutator relation for an operator $a[x,\omega]$ which depends on position $x$ and frequency $\omega$ $$ \left[a[x,\omega],a^{\dagger}[x^{\prime},\omega^{\prime}]\right]=\...
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Notation for rule of thumb, without breaking dimensional homogeneity?

I'd like to know how to write rules of thumb in a concise way, without breaking dimensional homogeneity. For example, if a runner has an average speed of ~10 km / h, an approximation of the covered ...
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When scaling down a universe, what is scaled down, and how to calculate gravity?

Assume I want to scale down Earth so that it fit into a 500x500 units (pixels) cartesian plane, at a scale of 1:1,000,000. Earth, with a radius of 6,371,000 meters, now has a radius of 6.371 units. ...
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What is unit system in this reduction process?

I have read "The Stopping and Range of Ions in Solids", which is published in 1985 about ion implantation. There is a equation in P.53 : $$ \varepsilon=\frac{32.53M_2E_0}{Z_1Z_2(M_1+M_2)(Z_1^...
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Why are there two different units for charge; the coulomb and elementary charge? [closed]

Why are their two different units for $q$ charges?
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Units of damping terms for harmonic oscillator

I understand that in the equation of motion of a simple harmonic oscillator $\ddot{x} + \omega_0^2 x = 0$, $\omega_0$ has dimension inverse time. Since solutions are of the form $x(t) = A \cos (\...
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Why electrical current is base quantity instead of electrical charge? [duplicate]

I thought base quantities are defined as independent quantity. But I realized Electrical Current which usually notated as I for ...
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Transduction coefficient of an electromechanical system

I have been recently doing a physics experiment which requires me to determine the transduction coefficient of a speaker system, undergoing electromechanical resonance, in an AC circuit. The quantity ...
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Why are people using 'lightyear' as a measurement of time? [closed]

I came across 2 people in an open forum, who are college students, who that agree using the term 'lightyear' as a measurement of time is correct. Their context was "This country's technology is ...
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Unit of a log normal probability density function

How do I find the unit of a log-normal probability density function?
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Ratio of thermal energy in a parcel of water between two time periods (metric vs imperial units)

I am having a problem figuring out something that should be quite basic with determining the ratio of the thermal energy content of a parcel of water (let's say $1 kg$) in between two time periods and ...
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On "cosmic flux" units

I've trouble understanding the following graph, taken from Wikipedia: It's supposed to show the cosmic ray flux vs particle energy. I've never seen a "flux" written in these units... Why ${...
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Second functional derivative and its units

Say I have a functional $I[\phi,g]$ with $\phi(p)$ and $g(p)$ functions from $\mathbb{R} \to \mathbb{R}$. Also say that this functional obeys the property: $$\frac{\delta I}{\delta g(p)} = -(g(p))^{-1}...
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Do squared units grow in size or shrink in size if the value can be represented by a different unit?

I was doing a very simple equation, $\frac{1}{2}kx^{2}$, when I realized that, if I represented the distance in centimeters, $x^2$ would grow in size (because x is 10 centimeters), but if I ...
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Conversion factors derivation

Unit conversion chart Queries regarding MKS to CGS system for the following formulas : Force $=$ Newton (MKS), Dynes (CGS) $$\mathrm {1\ N = 10^5 \ dynes}$$ Work $=$ Joule (MKS), Ergs (CGS) $$\...
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Imperial units - mass and force

I was rudely informed on an answer here that 1 lb is a force and I 'didn't understand' mass. (I am not interested in relative merits of systems of units - only dimensions..) Now - we know that Force ...
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Units in vector spaces

I am confusing myself about where physical quantities become mathematical objects. Where does one end and the other begin? E.g. displacement $\vec{s}$. A displacement is a physical quantity that can ...
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2 answers
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Electromagnetism using differential forms, question about names and units

When formulating classical electromagnetism using differential forms, Maxwell's equations can be written as $$ \begin{align} dD &= \rho \\ dB &= 0 \\ dE &= -\dot{B} \\ dH &...
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Calculating photographic exposure - confused about luminance, illuminance, luminosity etc

On first glance this sounds like a photography SE question, but it's more concerned with physical measurement of luminosity, luminance etc - the photographic application of the value calculated is ...
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What units to put on axis when logarithmic?

Currently I'm making some plots for my colleted data set from my conducted physics experiment. In one of the cases, I'm actually plotting the logarithmic relation between the dependent and independent ...
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When we set $c=1$ and $\hbar=1$, why is energy still measured in $eV$?

When we set $c=1$ and $\hbar=1$, we often see in particle physics that mass and energy are expressed in terms of $eV$. This doesn't make sense to me. If we are choosing a new unit system where for ...
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Understanding the units in an expression

I am reading an article, and I saw this expression in Eq.5: $$\dot{u} \sim \frac{\psi}{L} \sim (\frac{H^{-1}}{L})H\psi\sim (\frac{40~\rm{kpc}}{L})(\frac{\psi}{b})H$$ Where $u$ is the velocity, $L$ is ...
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Why aren't liters a SI Unit? And why isn't there a unit for volume?

In the International System of Units, there is the second for time, the metre for length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for density, and ...
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How do units work when integrating a distribution that has units?

In case some want more context, the source which I'm using (could be wrong...?) is: https://arxiv.org/abs/physics/0202029 (Eqs. 2,5,7) The equations of concern are: $$\sigma_a(\omega) = \sigma_0 g(\...
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What is the gravitational constant in 5D?

I am trying to find the energy density for a given spacetime using Einstein's Equation $G_{\mu\nu}=\kappa T_{\mu\nu}$. I am trying to do this in 5D and with restored SI units, but I am having trouble ...
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Can the Maximon Equation be adapted to calculate the pair production cross section for different particles?

The Maximon equation describes the cross section for pair production near matter. It takes the form ${\displaystyle \sigma _{pair}=Z^{2}\alpha r_{e}^{2}{\frac {2\pi }{3}}{\biggl (}{\frac {k-2}{k}}{\...
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Why the parsec (pc) is still a good cosmological definition in the curved spacetime in a large scale of universe?

The parsec (pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to 3.26 light-years or 206,000 astronomical units (au), i....
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Dimensionally, how does this have units of velocity: $2 q I/(m c^2)$

I'm reading through a paper about charged particle trajectories in non-uniform magnetic fields (Drift velocity of charged particles in magnetic fields and its relation to the direction of the source ...
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Volume in spherical units

(I asked this questions in Mathematics section but there were no answers.) I'm working on Cavendish's original analysis of his experiment. Cavendish does not use equations or standard units. For ...
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In the FLRW solutions for the EFE, what is $T_{00}$ (in SI)?

I am attempting to create a Mathematica solver for the Einstein Field Equations (EFE) that will work for SI and Natural Units and any sign convention. It works for Natural Units, but when I try ...
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Is there a difference between a 'pure number' and dimensionless quantity

I see dimensionless quantities described as 'pure numbers' I mostly understand this in terms of ratios (angles, a lot of dimensionless constants) as we are not really counting or measuring anything ...
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Why are there just 3 main units ($L$,$T$,$M$) in physics?

Most physics books define physical units in terms of length, time and mass. Some books add temperature. And yes, the SI unit system has 7 base units, but some are clearly redundant. Why are exactly ...
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Does it make sense to create a spacetime diagram in respect to another velocity besides the speed of light?

I'm trying to understand the application of special relativity into things where it's velocity might be none regular units. Just for argument sake, let's say that the distance is measured in some unit ...
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Can Candela be infinite?

We know that nothing can speed up beyond the speed of light. Which means the speed of light (somewhere around $3 \times 10^8$ is the upperbound of speed). Now I wonder if there is the same upper bound ...
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Question about the units of an operator related to the time evolution operator

Let $U(t, t_0)$ be the unitary time evolution operator. Define an operator $\Lambda (t):= \partial_t [U(t, t_0)] U^\dagger (t, t_0)$. This operator turns out to be independent of $t_0$. Now, the ...
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Why do we consider some quantities 'dimensionless'?

It seems strange to define some quantities such as countable objects or the unit mol to be 'dimensionless'. For me, It leads to many sources of confusion, do we consider a dimensional quantity with ...
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Why is kelvin used for Energy Separation in atoms?

I have been reading a 1974 paper on the anisotropy of Sm$^{3+}$ ions, in which the authors say the following: IN THE series of trivalent rare-earth ions, Sm$^{3+}$ is unique in the sense that the ...
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What happened to the Planck charge on Wikipedia? [closed]

Wikipedia used to have a nice article about the Planck units, with contributions made directly by Don Page. I recently visited the current article and the Planck charge kind of disappeared. I also saw ...
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Determine the unit of raw number expressions that also convert between units

In a program code that calculates physical quantities while omitting their units, I found the following calculation: ...
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Good book/resource/chapters on the foundations and science of accuracy, precision, and measurement?

I guess measurement and accuracy is a science, and thus, I assume there's foundations and universal theory that can be learned from scratch, independently of international conventions used, just like ...
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Could you have a quartic or square degree Celsius or other degree on a temperature scale raised to any power?

Could you have a quartic or square degree Celsius or other degree on a temperature scale raised to any power? The units of the Stefan-Boltzmann constant are watts per square meter per quartic kelvin, ...
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