# Questions tagged [units]

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

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### Why is 1000 micrometer not a correct representation of a prefix?

Why is 1000 micrometer not a correct representation of a prefix? I ask because I recently took an entrance exam with a multiple-choice question which went along the lines of which of the following is ...
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### Units of energy and frequency

I read a paper about using femtosecond laser to process an atom. The units used in the paper bothered me. I have four questions. (1) Why the unit of energy is cm$^{-1}$? (2) It seems that the author ...
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### What should be the unit of mass while calculating centre of mass?

Can it be in any unit ? Can it be in grams, Kilograms or Unified atomic mass( to calculate centre of mass of a compound) Or should I convert them to kg and then proceed?
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### How can I determine the value of the electric permittivity my arbritrary unit system?

The unit system Working with electromagnetic fields, I define a unit system where the unit of length is $l_0$, and the unit of speed is $v_0$. In other words, I introduce a system of semi-normalized ...
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### The units of unified atomic mass

There is something I don't understand about the units of unified atomic mass. I have seen on Khan Academy that $1$ unified atomic mass ($u$) is equal to $1.6605\times 10^{-27}$ kg. But after 2 videos ...
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### Some questions in Newtonian gravitational force derivation

I came across a good website that explains how Newton derived his formula of gravitational force click here Why is $\frac{k}{4\pi ^2}=\frac{c}{M}$ and $f=(kmM)/r^2$ not $(4\pi^2)/r^2\sqrt{MmcC}$? ...
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### Unit Analysis Question: Possible to Solve [closed]

A nautical mile is the distance traveled in moving through one minute of latitude. A ship which is sailing at a speed of five knots travels five nautical miles in one hour. Two hundred years ago, the ...
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### Why does a right-circular cylinder helps reduce surface area of the former International Prototype of Kilograms

I read on Wikipedia that right-circular cylinder shape helps reduce surface area of the former IPK, but could not find an explanation as to why. So how does such shape helps reduce its surface area? ...
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### What does the derived unit “square coulomb” quantify?

As a square meter (m$^2$) quantifies area and not length, what does a square coulomb (C$^2$) quantify?
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### Units of $\hat{a}$ and $\hat{a}^\dagger$ in discrete vs continuous $k$ and normalization

Consider the quantization of the electromagnetic field. In the discrete case, given in Wikipedia, the operators $\hat{a}$ and $\hat{a}^\dagger$ are dimensionless $$[\hat{a}]=[\hat{a}^\dagger] = 1,$$ ...
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### What does the “area” represent in the luminance of the sky?

Wikipedia and plenty of other sources give values for the luminance of the sky, of e.g. $\mathrm{2\ kcd/m^2}$. What area is the denominator representing here? How can something like the sky, that ...
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### How to get the correct (Gaussian) units for electric and magnetic fields?

Friedman and Susskind in their Special Relativity and Classical Field Theory use the following Lagrangian for a charged particle in electromagnetic field characterized by the 4-vector potential $A_\mu$...
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### Formula gives different results if radians or degrees are used?

The formula to describe the angle $\theta$ in a conical pendulum is: $$\theta = sin^{-1} \left( \frac{g}{l\omega^2}\right)$$ This gives different results depending on if you use radians or degrees. ...
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### What is the constant in $F=kma$ called?

I understand fully where the constant comes from and why it is defined as $k=1\ N\ kg^{-1}\ m^{-1}\ s^2$ But does it have an official name? If I were to give it a name I suppose I would maybe call it ...
I have a chart that displays conformal time on the vertical axis, comoving distance on the horizontal axis. The values are in units of billions of years (Gyr), but scaled logarithmically such that $$... 0answers 8 views ### How to make the Coulomb potential return energy per mole? I'm trying to adjust an electrostatic potential curve obtained via DFT calculations to the Coulomb potential equation to obtain the charges for a given atom. I know that the coulomb potential is given ... 1answer 22 views ### Properties of gas and mixtures Is specific heat at constant pressure for an ideal gas has unit always Joule/kg-K or can be Joule/kg-°C specifically for ideal gas only? 3answers 219 views ### Units of observables in quantum mechanics Observables in quantum mechanics are described by Hermitian operators \hat A: V \to V, where V is the Hilbert space of states. Examples include the x-coordinate operator \hat x, the x-... 1answer 39 views ### Which version of the cgs system in publication from 1983 I am currently implementing the model proposed in this publication (1983). I already figured out, that it probably uses cgs units. (The units of 1/\epsilon_0 would be missing in eq. (24,25), if it ... 1answer 37 views ### What is 'parsecs per cubic centimeters' in a radio source's dispersion measure? The units of 'parsecs per cubic centimeter' is really hurting my brain... Could someone please explain this weird astronomical unit? 2answers 46 views ### Is there any reason why N\ kg^{-1} shouldn't be used as the units for acceleration? When doing a calculation involving a force of F=1000 N on a mass of m=100 kg we use the formula a=\frac{F}{m}$$a=\frac{F}{m}=\frac{1000\ N}{100\ kg}=10\ N\ kg^{-1}$$Is there any reason why I ... 1answer 73 views ### Does “\rm m/s” mean the same thing when used for instantaneous velocity and for mean velocity? The following question on Philosophy SE https://philosophy.stackexchange.com/q/73366/ relies on this "given" "suppose that the instantaneous velocity of object A is 1m/s and that the mean ... 6answers 497 views ### Clarification of “inertial mass” explanation I am currently studying Classical Mechanics, 5th edition, by Kibble and Berkshire. Chapter 1.3 The concepts of Mass and Force says the following: Clearly, we can compare the inertial masses of two ... 2answers 188 views ### Why does \epsilon_0=1 in CGS units? This Wikipedia article gives a table of certain constants in different systems of units. I noticed that in Gaussian and electrostatic CGS the value of \epsilon_0 equals the dimensionless 1. I ... 1answer 22 views ### Converting units, for the magnetic moment I found, that magnetic moment is measured by \rm J/T, and equals magnetization times volume:$$\vec{m}=\vec{M}VMagnetization, also equals magnetic susceptibility times external magnetic field: ... 1answer 66 views ### Which physical qualities have only one unit of measurement? Which physical qualities have only one unit of measurement? One example is frequency, Hertz. Are there others? 2answers 55 views ### What are the accepted abbreviations for Million Years and Billion Years? I'm putting together some charts and the time axis in one shows billions of years, the time axis in another shows millions of years. I've seen in various publications my and myr (also ma) for ... 4answers 63 views ### Why is surface tension measured in units of milliNewtons per meter? Rather than square meter(s)? Why is liquid surface tension written in units of mN/m, or milliNewtons per meter? The related concept of surface energy for solids uses units of milliJoules per square meter. 1answer 57 views ### Proving base Units of SI are not enough for numerical computations [closed] I have been working on a way to prove that the base unit of SI is not enough for numerical computations to make sense. What I mean by that is let's say you're given units of angular velocity to be [1/... 1answer 65 views ### How do units 'change' when we move to the language of differential forms? Consider a 2D Euclidean vector as we're taught in first year: p = x \>\hat{i} + y \> \hat{j}  where x and y are in meters. If one goes looking for the units of a unit vector they will be told ... 0answers 12 views ### Units of angular speed vs linear speed [duplicate] I'm studying pendulums, and the units have me a bit confused. In a pendulum, Iw^2=mgL. Putting together the units of the left side of the equation, we get gm^2 (rads^-1)^2=g(m^2)(s^-2)(rad^2). But ... 1answer 28 views ### Units of the Boltzmann constant in 2 dimensions I am answering a question in which volume is given as m^2 which I assume means that the question is considering a 2 dimensional box for the volume. I am trying to calculate N using the given ... 0answers 37 views ### Confusion with units of angular velocity [duplicate] I know that the SI unit of angular velocity is s^{-1} (because radians or angle measure is dimensionless). I encountered a question that said: Given angular velocity = 12 \, s^{-1} and angular ... 0answers 18 views ### Why are luminous intensity, luminous flux and illuminance physical quantities if they are based on the sensitivity of the human eye? If luminous intensity and other derived quantities are based on the luminosity function, which is based on the sensitivity of the human eye, why are they physical quantities? Why is luminous intensity ... 1answer 222 views ### Is there a need for the unit mole? [duplicate] If 1 mole of X is approximately 6.02 \cdot 10^{23} X, why is it a unit? How does it have the characteristics of a unit? Is it just a different way of writing the Avogadro's constant? Does amount ... 0answers 31 views ### Is there a use of the SI units gray, sievert and katal in pure physics Since the gray and the sievert are associated with relative biological effectiveness of the radiation and the katal is associated with catalytic activity, do the gray (Gy), sievert (Sv) and katal (kat)... 2answers 47 views ### Converting the Gravitational Constant [closed] Hello all and thank you for reading. I am creating a program in Unity where I recreate the earth-moon orbit. Unity struggles with numbers so large when I write code in meters and kilograms so I made ... 2answers 138 views ### Convert SI units into natural units I have a simulation program which uses cgs-units. Additionally, I defined a natural system of units: \begin{align} \text{L} = [R], \quad \text{M} = \left[ \frac{e^2}{p^2 R^9} \right], \quad \text{T} =... 1answer 50 views ### Calculating the units of pressure in General Relativity, knowing G=M=c=1 I'm trying to figure out how large Pressure units compared to the standard CGS model is when taken G=M=c=1 What I have been thinking is:\dfrac{GM\rho}{r^2} = - \nabla P$$or$$\|G\| \mathrm{\...
Consider the function of temperature as a function of position, $T(x,y,z)$. Is the argument of the function dimensionless? I mean, when we want to find the value of the function at the position $x=1m$,...