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Questions tagged [units]

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

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Coordinates in 1970 Labeyrie article

I'm reading the 1970 article by Labeyrie on speckles in astronomy and I encountered a small problem. The author uses two sets of coordinates, $(\alpha, \beta)$ and $(x, y)$, connected by Fourier ...
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What is the unit of polarization mode dispersion?

I calculated the differential group delay (DGD) from measured data following a chapter in the book "Polarization Optics in Telecommunication" by Jay Damask. Basically, I measured a unitary matrix $U(...
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What are the units for state vectors in QM? [duplicate]

Specifically, it seems that a state vector should be dimensionless because: $| \langle \psi | \psi \rangle |^2$ is a probability which is dimensionless However, I find myself doing manipulations ...
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Meaning of units in the Heisenberg Uncertainty Principle

So we have the inequality $\Delta x\,\Delta p\geq \hbar/2$ Why is the uncertainty of position in meters? Isn't uncertainty measured in probabiliies? Does it make sense to say that the uncertainty in ...
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Is a unit vector really unitless and dimensionless?

According to my textbooks, a unit vector has no units and no dimensions, but is only used to specify direction. It only shows the orientation of a corresponding vector in space. I think it's true, or ...
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Electromagnetic four-potential plane waves expansion in SI units

In Mandl's book Quantum Field theory the expansion of the electromagnetic field is given by $$A^{\mu}(x)=\sum_{r,\vec{k}}\left(\frac{\hbar c^2}{2V\omega_{\vec{k}}}\right)^{1/2}\varepsilon^{\mu}_r(\vec{...
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Are the units of energy the same in higher dimensions?

In 3 spatial dimensions, $$[E] = [ML^2 T^{-2}]$$ Would it change in higher dimensions? If yes, then what would be the dimensions for 4 spatial dimensions?
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Significant figures in multiplication with units

Why does it make sense to round to the smallest significant figure instead to the largest unit? If I have one measurement made to the nearest millimetre and another to the nearest picometre then why ...
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In the value of gas constant $R$, what kind of mole is it?

Wikipedia gives $$R=8.3144598(48)\, \rm J\,mol^{−1}\,K^{−1}$$ But I want to ask how is it possible to write $\mathrm{mol}$ without a suffix? I mean, we must determine if we have $1\ \mathrm{mol}$ of ...
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What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? [duplicate]

What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? For example, $1 \:\rm m/s$ mean that each second, we make one meter. Also, $1\:\rm m/s^2$ mean that each second the speed ...
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Expressing the conversion from units of time to units of space in special relativity rigorously

In their book Spacetime Physics, Taylor and Wheeler stress the analogy of the speed of light $c$ to a conversion factor $k$ which converts between miles and meters and subsequently convert freely ...
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mathematically explain why add operators with different physical unit is wrong?

Suppose I have two operators $J^2$ and$J_z$ where they represent the length of angular momentum and its $z$ component respectively. Sure, it's legal to write new operators like $J^2-J_z^2$ or $J_x+...
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Why Planck's constant is so small? [duplicate]

Why Planck's constant is so small? If $h=10^{-10}$ then what have been happened? Or $h=1$?
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3answers
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What does the unit “kcal/mol” mean?

I recently encountered units of energy written as $``\mathrm{kJ}/\mathrm{mol}"$ or $`` \mathrm{kcal} / \mathrm{mol} "$. I'm aware of the meanings of $`` \mathrm{kJ} "$ and $`` \mathrm{mol} " , $ ...
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How do I add measurement units to a power-function relationship like $y = 0.17x^{0.52}$?

I have the equation $y = 0.17x^{0.52}$, where the units on $x$ are $\rm cm$ and the units on $y$ are seconds. I can't figure out how to put units on the constants so that they work out and I get the ...
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I'm confused about electric flux?

In a previous physics class, I learned that the electric flux was $\vec{E}\cdot\vec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and ...
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Intuition about the congruence of readings of Celsius and Fahrenheit scales at -40°C [closed]

At -40°C temperature, the Fahrenheit scale also shows -40°F. But how is this ever possible? They are two different scales! What's the intuition behind this?
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Mass (as a unit) has no physical property [closed]

Einstein's GR or Newton's equation uses mass as unit or number. How can it cause gravity (physical phenomena)? For any physical phenomena to occur, there must be physical/chemical/biological/etc. ...
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Coincidental relation between ratio of masses, lengths and time intervals in the universe

The ratio between the largest and smallest lengths in the universe is about 10^41 and it's the same with time intervals. But for masses the ratio is about (10^41)^2. Is this purely a coincident or is ...
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1answer
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Can this quantity defined by exponentiating lengths be meaningful?

I just read Accurate predictions of coexistence in natural systems require the inclusion of facilitative interactions and environmental dependency in which they defined the following property:$^1$ $$\...
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1answer
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Is there an MKS unit system in which electric and magnetic fields have the same measurement unit?

I'd like to know if there's an MKS unit system in which electric and magnetic fields have the same measurement unit. I couldn't find anything like that on the internet. Does that system exist? Do ...
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What is the value of absolute zero: $-273.15\ \rm °C$ or $-273.16\ \rm °C$?

What is the value of absolute zero? 0K= -273.15 °C Or -273.16 °C It has been confused in different scientific scriptures. The first definition on Dictionary.com, for example.
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Is it a coincidence that 1 liter water has a mass of 1 kg while 1 cubic meter has 1000 liters of water?

1 Cubic Meter has 1000 liters of liquid. Meter is a unit independent of Kilogram. Then why does 1 liter of water at max density (4°C) have a mass of 1 Kg?Is it a mere coincidence?
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Geometrized units in Wald

I am trying to follow a derivation in this paper from Wald Specifically, at the end of the paper, just under Eq. 4.7 there is given the equation $$ Q/m \leq 2 B_0 m$$ where $Q$ is the system ...
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Why are the dimensions of escape velocity correct?

How does this formula work, from a dimensional analysis perspective? $$ v_\text{escape} = \sqrt{\frac{2GM}{R}}$$ The way I'm thinking about it is that $G$ is in units $\text{N} \cdot \text{m}^2/\...
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What does “as small as a fraction of an angstrom” mean?

I was reading my school textbook in which the following statement was given: The resolution of such an electron microscope is limited finally by the fact that electrons can also behave as waves! (...
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How to put $c$ back into relativistic equations?

Many books set the speed of light $c=1$ for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though $G$ is still left as a constant): $$\begin{align} \mathrm{d}\tau^2 &...
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Stoney Units vs Planck Units

Why are the Stoney Units (excluding elementary charge) still shown to be different than the Planck Units when they can be divided by the square root of the fine structure constant which would make ...
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Does the magnitude of a physical quantity have units or is it just a plain number?

Does the magnitude of a physical quantity have units? For example, if a velocity vector is $36\ \mathrm{m\,s^{-1}}\ \hat{u}$, is its magnitude $36\ \mathrm{m\,s^{-1}}$ or just $36$? Also why?
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Question about Radian as a unit

I'm having a hard time trying to understand the units between angular velocity and basic velocity of a circle. For angular velocity the units are Radian(s) per second(s) or degree(s) per second(s). ...
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Pressure unit computation (feet of mercury, but applies also to foot of water..) [closed]

Grr this question makes me crazy. Here you can see that ftHg = 13595.1 kg/m3 × 1 ft × ɡ0 = ≈ 4.063666×104 Pa. (= 40636.664 Pa) https://en.wikipedia.org/wiki/Conversion_of_units (Pressure or ...
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Is the International System of Units complete?

Are there any known (measurable continuous) physical quantities, which are neither base quantities of SI, nor are derivable from the base quantities? In other words, are there any quantities which ...
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Why are “degrees” and “bytes” not considered base units

From Wikipedia: The SI base units and their physical quantities are the metre for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for ...
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What actually is 1 Coulomb ? Is it number of electrons or the amount of force?

(Pardon my English). My question is very simple (so simple that it might get the "on hold" honour). Anyways, since I've just started my highschool, only to land in the beautiful world of electricity ...
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1answer
55 views

Does it make sense to multiply a unit by a negative number?

I was thinking about the way our system of units of work, and I realized that we have been multiplying units (such as for lengths) by negative numbers, when dealing with vector quantities; positive ...
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3answers
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Magnetic $H$ field unit in cgs system

I'm studying an old E&M textbook which uses cgs unit system. I'm re-writing the formulas in SI unit. The book says $\vec{H}=\vec{B}-4\pi\vec{M}$. So I guessed that $H$ should have same unit as $...
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Downsampling the wavelength spacing of spectral radiance

I have spectral radiance measurements, $L_e$, that I need to downsample, and I want to make sure I do this correctly. Let's say the measurements are a constant value of $5\times 10^{-3}\: \rm W \: m^{-...
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1answer
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Units caculation in the article don't match for reynolds numbers higher than 1

The article discusses the forces acting on a falling object in respect to the drag forces and reynolds numbers. The article suggests for varying Reynolds numbers, the force of drag equation is written ...
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Why does this paper use 1/cm for units of frequency?

Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency. Here is an excerpt: It doesn't seem like wave number, as they clearly call it frequency. What's going on here? $^*$ ...
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Infinite plane gravity: what is “mass density per unit area”?

Recently I learned that the gravity of an infinity plane is independent of the distance from that plane. In fact it is $$g = 2\pi G \sigma$$ where $\sigma$ is "the mass density of the plane per unit ...
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1answer
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How can we use zero in physics [duplicate]

Is better to say the e.g. kinetic energy is 0 joule or kinetic energy is 0 ? since 0*joule equals 0.Is a mathematical concept behind because in many books i find both ways.
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4answers
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Converting part of a compound unit

I am working with several different datasets with different units. I want to convert the distances to mm for comparison. The units I'm dealing with are $\mathrm{kg/m^2/s}$, $\mathrm{mm/day}$, and $\...
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1answer
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What does pc(eV) = 300 Br(G cm) mean?

In the January 1983 issue of the American Journal of Physics, Edward Purcell published a one-page "Round-Number Handbook of Physics" (see e.g. http://lemeshko.blogspot.com/2008/06/one-page-round-...
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Why is Scan Rate Measured in Hz, not Hz/s?

Spectrometers have a specification called scan rate. As spectrometers measure spectrum, one would think the units of scan rate would be like Hz/s - meaning, the bandwidth scanned per unit time. Like ...
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How to convert bars to meters head?

I am trying to convert 1 bar to meters to come up with a conversion factor. Thus, 1 bar = x meters head What is x? From my computations I got something like ...
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Keeping track of units

I'm not quite sure how keep track of physical units when differentiaion is involved. I find it important to keep track of units because I want to be able to check the units afterwards. I will discuss ...
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1answer
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How can I convert spectral irradiance to spectral radiance [closed]

I have information on the spectral irradiance incoming from the sun at the top of the atmosphere in units of $\rm mW\ m^{-2}\ nm^{-1} $. The photons hit a hypothetical surface on the earth with 0.3 ...
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1answer
59 views

Is there a rule on which order to write derived SI units?

I noticed from https://en.wikipedia.org/wiki/SI_derived_unit than derived units have to be written in a specific order. For example Newton Metre is written: $$\text{m}^2⋅\text{kg}⋅\text{s}^{−2}$$ ...
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3answers
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What is the unit for work done?

My textbook's equation for work done is: work done = force * distance So this means that the unit should be Nm. However, when I researched on Google, a lot of people were saying that the unit is J....
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Vector units with different unit in each component

I'm used to encounter units that come from product or division of units, such that $m/s$ or $kg\cdot m\cdot s^{-2}$. However, I have never seen a unit defined as a sum of units, for instance, $m+J$. I ...