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Questions tagged [units]

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

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Units after integrating a ratio metric: Point Source Transfer Mobility

I want to calculate the so called Line Source Transfer Mobility (LSTM) from 10 equispaced Point Source Transfer Mobilities (PSTM). The PSTM measures the response to an excitation, and it is defined ...
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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
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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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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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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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1answer
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Why $µ_0$ and $ε_0$ are not considered to be $4π$ and $1/4π$? [on hold]

I did some algebra... In Planck unit, if make $\mu_0 = 4\pi$ and $\epsilon_0 = \frac{1}{4\pi}$ you get: $$\mu_0 = 4\pi \cdot \frac{m_p l_p}{t_p^2 I_p^2} = 1.2566368452237765 \cdot 10^{-6} N \cdot A^...
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2answers
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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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Why is the length of the Kelvin unit of temperature equal to that of the Celsius unit? [duplicate]

The Celsius unit is arbitrarily defined, based on the boiling and freezing point of water. Is it a coincidence, then, that the SI unit of temperature Kelvin, which is used in all natural equations, ...
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4answers
2k views

The significance of kelvin as a unit of absolute temperature

$$PV=nRT$$ Where $P$ is pressure in pascals ($\text{Pa}$) $V$ is volume in cubic metres ($\text{m}^3$) $n$ is amount of substance in moles ($\text{mol}$) $R$ is the gas constant having units, joules ...
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1answer
32 views

What units are represented by pr - micrometer?

In studying column abundances, I often encounter the units $pr-\mu m$. What does this stand for? Part per micrometer? how can this be an abundance unit? Incredibility I cannot figure out what it ...
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44 views

Question about change SI unit, what is $h$ and how could they agree with anything? [closed]

I heard a speech about the changing SI unit, but then it got me concerned with a bunch of questions. Basically, they switched from sticks to some "fundamental constants". What is $h$? In the Metric ...
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6answers
151 views

Conversion of $R = 8317\ \mathrm{\frac{J}{kg\cdot mol\cdot K}} $ to $ 8317\ \mathrm{\frac{J}{kg\cdot mol\cdot {^\circ C}}}$

I'm trying to understand the unit conversions when one unit is obtained by shifting the value of another one by some constant. In particular, the unit conversions from Kelvin to Celsius scale: $$T(\...
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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
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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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Unit conversion in cosmology

In cosmology (Dodelson) , the natural unit is $\hbar=1, c=1, k_B=1 $. There the author writes the critical density of the universe $\rho_{cr}$ as \begin{align*} \rho_{cr}&=1.879 \ h^2\ \times 10^{-...
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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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2answers
72 views

The meaning of $\rm mHz$ and $\rm Hz^{1/2}$

If Hertz(Hz) is for once cycle per unit time what does mHz and $\sqrt{\text{Hz}}$ represents? I mean what is the physical manifestation of the a fractional power of a unit ?
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3answers
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Why is sound “loudness” measured in $dB$ instead of $[P]$?

From acoustics we know that sound is an elastic pressure wave. What our human senses perceive are "loudness" and "pitch" which are related to the amplitude and the frequency. While pitch can easily be ...
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0answers
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How to Measure Electric-Field Probe Sensitivity?

I am doing some reading on current methods for detecting electric fields. A figure of merit for the systems is, naturally, the minimum strength of field that can be measured, in units of Volts per ...
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1answer
51 views

Confusion on Centigrade/Celsius Scale

There came the centigrade scale. The issue was that many solid/liquid thermometric substances didn't respond to temperature linearly so different thermometers produced different results. This was ...
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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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1answer
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How can we compute the quantity $hc/e$ vs gauss and centimeter

In some textbook, authors mention that the amount of $hc/e$ equals to $4.136 \,\text{gauss}\times cm^2$. Where, $h$ and $c$ are Plank's constant and the speed of light respectively. Positive $e$ is ...
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1answer
74 views

Heaviside Vector Units

Became a little confused over last hour trying to understand the units of the Heaviside vector. So far I have come up with this from reading online: The Heaviside vector allows us to write the energy ...
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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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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
46 views

Virial radius of a collection of point masses

I am experimenting with multi body simulations in astronomy ($N$-body algorithms). It is customary to give the results in dimensionless units. One of them is a length unit, and the virial radius is ...
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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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Grasping systems of units

Perhaps it's that I've grown up with the SI system of units, but there's something about other unit systems that doesn't sit well with me. For example, Coulomb's law in Gaussian units can be written ...
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2answers
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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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After the redefinition of the units of fundamental physical quantities in 2019, will an uncertainty incur in the Universal constants values?

I am specifically interested in the following constants because being a student these are some of the most common constants that I face: $R$ (universal gas constant) Stefan constant Permeability of ...
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4answers
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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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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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Self inductance of a circular coil

I have read from my reference that the self inductance of a wire ring is derived in a non-trivial manner. I have copied an image off the result below, let me know if I should translate it to Latex. ...
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2answers
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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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2answers
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Factors of $c$ when giving masses in natural units?

I am starting a course on particle physics, and have been introduced to natural units. I am slightly confused, because we are using 'natural units', and yet masses are stated as, for instance, $139....
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1answer
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Is there no law which includes an addition of different types quantities? [duplicate]

I haerd that we cannot add two different types quantities. Is there no law which includes an addition of different types quantities? In the future, maybe we find a law like this $$F = \frac{\...
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2answers
159 views

Is there (or was there) a unit of electric current based on Avogadros number or Coulombs constant?

This has to do with the SI definition of the Ampere. Why the quantity $2*10^{-7} $ Newtons in particular? It would make more sense to define 1 Ampere = 1 mole of electron charge per second. Which ...
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2answers
58 views

Unit of pion-decay constant

In the natural unit system, the pion-decay constant $f_{\pi}$ is $92.4\:\rm MeV$. But I think that a decay constant should have a dimension of $[T]^{-1}$, where $[T]$ is the dimension of time. Then, ...
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1answer
22 views

Units of forcing function in the inhomogeneous wave equation

The units of the d'Alembertian are distance$^{-2}$. It should be the case that the inhomogeneous wave equation describing $$\square u = f$$ should have matching units on both sides. My understanding ...
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3answers
85 views

Confusion about Unit Systems

I was reading about Deuterium and came to know that its binding energy is $2.22$ MeV. I am curious whether this energy is in the natural unit system where $\hbar = c =1$. For instance, the energy ...
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0answers
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How to convert J/mol-K to BTU/mol-R manually?

How to convert $\frac{J}{mol-K}$ to $\frac{BTU}{mol-R}$ manually? Sorry for such a simple question, I am new to Physics and I'm getting confused when it comes to conversions of units. Please bear ...
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2answers
65 views

Is there any constant with unit meter-second?

I wanted to know if there exists a constant with a unit meter-time or say length-time. Dimensionally [LT]. I have searched browsed a lot. Is there any quantity arising with such a unit?
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Is length an extensive property?

From my experience, volume, surface and length are extensive properties. Indeed : the reunion of two cubes of 1 $m^3$ leads to a cube of 2 $m^3$ the reunion of two tiles of 1 $m^2$ leads to a tile ...
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2answers
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Is gravitational constant a rational number? [duplicate]

The question is the title. But I'm quite doubtful if this question is meaningful or not. Since this constant is obtained by experiment, we can never know its exact value, unlike $π$ or $e$. Is it ...
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1answer
73 views

Correct form of Lorentz force equation [duplicate]

When I was reading the first volume of the theoretical minimum by Leonard Susskind, I encountered upon this: But when I checked Griffiths and all my other electricity and magnetism books, it showed $...
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2answers
63 views

Scientific notation and usage thereof [closed]

I'm taking my first physics exam in university this Saturday, and I'm currently working on a practice exam. I got the answer 3.1MeV for a alpha-decay question, but the answer was 3100keV. I ...
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3answers
2k views

Why is torque sometimes reported in kg m, instead of the usual N m?

On various websites I see torque expressed as $\rm kg\: m$, but I was always thought that torque is $\rm N\:m$ or $\rm kg\: m^2/s^2$. These are clearly not the same, so why are they called the same, ...