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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1answer
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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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1answer
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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 luminosity unit “Rayleigh” mean?

I read some articles which adopted "Rayleigh" as luminosity unit, what does it means? How bright is "1 Rayleigh"? How could I convert it to normal unit such as photon$\cdot$cm$^{-2}...
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Why not to multiply with $g$ when doing sums in the unit $\rm kgf$? [closed]

My book told me a thing to keep in mind while doing upthrust sums in $\rm kgf$. It's stated as follows: (See point number 2) Can you please explain why not to multiply with $g$? Also I am giving ...
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Is Nm the same unit of torque as mN?

A couple of days ago, I noticed that the torque unit used by my teachers is $mN$, and while reading on the internet it came to my notice that in all textbooks the official unit is $Nm$. I asked one ...
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When discussing discrepancy and its relationship to uncertainty, how much is acceptable?

I am new to physics and am learning about discrepancy and uncertainty. The below question is a Check Your Understanding Question, DISCLAIMER: NOT HOMEWORK. The way I went about solving the problem was ...
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1answer
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Lorentz Force Dimension Analysis [closed]

A charged particle in the presence of charges and currents experiences a force due to electric (E) and magnetic (B) fields. Is is described by the Lorentz force: $$F = e (E + v × B )$$ where e is ...
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Units in curvilinear (e.g. polar) coordinate systems [closed]

Let’s say that someone measures the distance from a rocket to the earth's surface to be equal to $h=10[m]$ (meters) at time $t=5[s]$ (seconds) (in a Cartesian coordinate system) - so our vector with ...
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2answers
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Are the amplitudes of the electric field and the magnetic field of an electromagnetic wave equal?

In an electromagnetic wave, is the maximum amplitude of the electric field the same as that of the magnetic field? I ask this question which may seem silly because on all the diagrams representing an ...
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1answer
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What does $\rm fT/Hz^{0.5}$ mean?

I was browsing the Wikipedia page for "Magnometer" and saw the figure that a caesium vapour magnetometer has a sensitivity of $300 \rm\ fT/Hz^{0.5}.$ I understand femtotesla but I am ...
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How to derive the formula for heat produced due to electricity correctly from Joule's laws for heating?

From Joule's laws, we get this: $$H\propto I^{2}Rt$$ $$\implies H = KI^{2}Rt ...(i)$$ Now, we have to find/define the value of K. According to my book, when $1A$ of current passes through a conductor ...
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1answer
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Regarding difference in dimensions of a physical quantity in different unit systems [duplicate]

So, Coulomb's Law states that $F_e = k\dfrac{q_1q_2}{R^2}$, where $F_e$ is the force of attraction between two charged particles of magnitude $q_1$ and $q_2$, where the distance between them is $R$. $...
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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 ...
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How would you label an axis that is Log base 10 in Gyr?

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 $$...
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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 ...
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1answer
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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?
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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 $x$-...
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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 ...
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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?
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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 ...
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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 $1$m/s and that the mean ...
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6answers
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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 ...
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2answers
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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 ...
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1answer
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Converting units, for the magnetic moment

I found, that magnetic moment is measured by $\rm J/T$, and equals magnetization times volume: $$\vec{m}=\vec{M}V$$ Magnetization, also equals magnetic susceptibility times external magnetic field: $...
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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?
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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 ...
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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.
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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/...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
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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)...
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2answers
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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 ...
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2answers
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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} =...
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1answer
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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{\...
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Can the argument of a function contain physical units?

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 $x=1m$,...

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