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

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Why do universal constants have the values they do?

This is meant to be a generic question of the type that we get repeatedly on this site, in different versions: The origin of the value of speed of light The gravitational constant G theoretically? ...
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4answers
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Fundamental question about dimensional analysis

In dimensional analysis, it does not make sense to, for instance, add together two numbers with different units together. Nor does it make sense to exponentiate two numbers with different units (or ...
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965 views

units and nature

I am wondering whether the five$^1$ units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man? Is the number of linearly independent units a ...
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11answers
10k views

What is the logarithm of a kilometer? Is it a dimensionless number?

In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is. Suppose I have something with length $L = 1 km$. $\lg L = \lg km$ It ...
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6answers
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Why isn't temperature measured in Joules?

If we set the Boltzmann constant to $1$, then entropy would just be $\ln \Omega$, temperature would be measured in $\text{joules}$ ($\,\text{J}\,$), and average kinetic energy would be an integer ...
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10answers
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What exactly is a kilogram-meter?

This question isn't just about kilogram-meters, it's about multiplied units in general. I have a good mental conception of divided units, e.g. meters per second or grams per cubic meter. Meters per ...
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2answers
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Square bracket notation for dimensions and units: usage and conventions

One of the most useful tools in dimensional analysis is the use of square brackets around some physical quantity $q$ to denote its dimension as $$[q].$$ However, the precise meaning of this symbol ...
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7answers
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Why is there a factor of $4\pi$ in certain force equations?

I mean to ask why there is $4\pi$ present in force equations governing electricity? Though all objects in universe are not spherical and circular, the constant of proportionality in both equations ...
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8answers
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Is there a symbol for “unitless”?

I'm making a table where columns are labelled with the property and the units it's measured in: Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc... I'd like not to write "unitless" ...
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9answers
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Why is torque not measured in Joules?

Recently, I was doing my homework and I found out that Torque can be calculated using $\tau = rF$. This means the units of torque are Newton meters. Energy is also measured in Newton meters which are ...
3
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3answers
986 views

What is the meaning of speed of light $c$ in $E=mc^2$?

$E=mc^2$ is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is ...
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7answers
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Why are radians more natural than any other angle unit?

I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
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4answers
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Simple Harmonic Motion - What are the units for $\omega_0$?

I'm trying to understand the units in: $$mx''+kx=0$$ And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$ Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring ...
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2answers
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Relating milliampere-hours to watt-hours for batteries

I've seen many batteries that are measured in milliampere hours (mAh), while others are measured in watt hours (wh). How can I convert them between each other so that I can actually compare them? It's ...
14
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4answers
723 views

Why isn't it $E \approx 27.642 \times mc^2$?

Sorry for the strange question, but why is it that many of the most important physical equations don't have ugly numbers (i.e., "arbitrary" irrational factors) to line up both sides? Why can so many ...
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1answer
202 views

CGS Units for Magnetism

Why does the formula for magnetic field force include the speed of light in the denominator in cgs units? Where does the extra $c$ go in SI units?
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Is negative 20 psi / 1.5 bar possible?

If I understand correctly, negative pressure usually means relative pressure: the difference between inside and outside. If outside is normal (1 bar, 15 psi, 100 kPa etc), how low can the (relative) ...
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3answers
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How can I understand counterintuitive units like $\text{s}^2$?

One of the things I never understood, but was too afraid to ask is this: how should I think of things like $\frac{\text{kg}}{\text{s}^2}$. What exactly is a square second? Square foot makes sense to ...
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5answers
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What do units like joule * seconds imply?

I can easily understand what divisive units imply, but not what multiplicative units imply. What I mean is, when I read "$12 \:\mathrm{eggs/carton}$", I mentally convert it to, "There are 12 eggs ...
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2answers
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Unit of torque with radians?

Usually, the angular frequency $\omega$ is given in $\mathrm{1/s}$. I find it more consistent to give it in $\mathrm{rad/s}$. For the angular momentum $L$ is then given in $\mathrm{rad \cdot kg \cdot ...
3
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3answers
835 views

convert units for spectral irradiance

How can I convert $$ W m^{-2} sr^{-1} nmm^{-1} $$ to $$ W m^{-2} nm^{-1} $$ I have the following matlab code to illustrate the spectral energy distribution of solar radiation: ...
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5answers
425 views

Is the number 1 a unit?

In dimensionless analysis, coefficients of quantities which have the same unit for numerator and denominator are said to be dimensionless. I feel the word dimensionless is actually wrong and should be ...
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2answers
2k views

What are the units of the quantities in the Einstein field equation?

The Einstein field equations (EFE) may be written in the form: $$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi G}{c^4}T_{\mu\nu}$$ where the units of the gravitational constant $G$ ...
3
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2answers
417 views

Exponential or logarithm of a dimensionful quantity?

I have a unit measure, say, seconds, $s$. Furthermore let's say I have a dimensionful quantity $r$ that is measure in seconds, $s$. What is the unit measure of $e^r$? ($1/r$ is in $Hz$.) My question ...
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3answers
150 views

Messed up units!

In the article, Environment-assisted quantum transport, $\gamma$ is a constant equal to $2\pi kT/\hbar*E_{R}/(\hbar\omega_{c})$ where $T$ is the temperature, $k$ is the Boltzmann constant. ...
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3answers
781 views

What does the decay constant mean?

In my curriculum, the decay constant is "the probability of decay per unit time" To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a ...
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2answers
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What is the physical interpretation of force times area?

I know that $\text{Force} \times \text{Distance = Work}$. But, what would be the physical meaning of $\text Force \times \text Area?$ Is such a quantity used in physics?
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1answer
461 views

What are the proposed realizations in the New SI for the kilogram, ampere, kelvin and mole?

The metrology world is currently in the middle of overhauling the definitions of the SI units to reflect the recent technological advances that enable us to get much more precise values for the ...
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4answers
478 views

How can there be a quantum field theory that predicts all particle masses?

Say I have a theory with only one (energy) scale, e.g. one given by the fundamental constants $$\epsilon=\sqrt{\dfrac{\hbar c^5}{G}}.$$ In this case, where I can't compare to something else, is ...
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3answers
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273 + degree Celsius = Kelvin. Why 273?

Temperature conversion: 273 + degree Celsius = Kelvin Actually why is that 273? How does one come up with this? My teacher mentioned Gann's law (not sure if this is the one) but I couldn't find ...
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8answers
698 views

What exactly are we doing when we set $c=1$?

I understand the idea of swapping from unit systems, say from ms$^{-1}$ to kms$^{-1}$, but why can we just delete the units altogether? My question is: what exactly are we doing when we say that ...
3
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2answers
143 views

Base quantities and charges

Is there an unit of color charge? I haven't found it, so I suppose that it doesn't exist, if this is right, why? Isn't it supposed that every measurable quantity can be expressed in terms of base ...
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Why is the absolute zero -273.15ºC?

I can't find an answer of why the lowest temperature is -273.15ºC. Is it deduced theoretically or is it experimental? An explanation is that when any gas volume tends to zero, the temperature will be ...
3
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1answer
347 views

Functional derivative and units

The both sides of below equation don't give the same units, e.g. $$ \frac{\delta}{\delta \phi (\tau)}\int_a^b \phi (\tau') d\tau'=1\;. $$ where $a<\tau<b$. To show this assume that the field ...
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3answers
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Centripetal acceleration units

I perform some basic calculation for circular motion. Formulas we get from school are: $v$ - Linear speed with the units m/s $r$ - Radius of curve in meters $\omega$ - Angular speed with the units ...
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1answer
213 views

Why are cgs units the norm in astrophysics?

Other physics communities, e.g. the particle physics one, have their own set of units, custom-tailored to their own needs. Now, the astrophysics community is somewhat similar, in that a lot of ...
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325 views

Factors of $c$ in the Hamiltonian for a charged particle in electromagnetic field

I've been looking for the Hamiltonian of a charged particle in an electromagnetic field, and I've found two slightly different expressions, which are as follows: $$H=\frac{1}{2m}(\vec{p}-q \vec{A})^2 ...
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3answers
290 views

100°C = 100 K =?

I'm in first year. Our class is in lesson " Heat and Thermodynamics". While solving a numerical problem of a reversible engine he told us that 100 degree Celsius is equal to 100 kelvin. I inquired but ...
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Is speed an intensive property?

I remember being taught in elementary physics that while it makes sense to add volumes, masses, or heat, it makes no sense to add temperatures. As I wanted to use that to illustate some other issue, ...
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2answers
534 views

Why is the absolute zero a rational number in Celcius?

From the question "Why is the absolute zero -273.15ºC?" I understood that 1°C is the 100th part of the difference of melting and boiling temperature of water (this is my high school physics, ...
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5answers
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Is anything actually 1 meter long (or 1kg of weight)?

I believe that no real objects are actually (exactly) 1 meter long, since for something to be 1.00000000... meters long, we would have to have the ability to measure with infinite precision. ...
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1answer
807 views

“Natural units” of mass

Gravitational attraction is given by $\frac{GMm}{r^2}$ while attraction due to electric charge is given by $\frac{q_1 q_2}{r^2}$. Why does gravity need a constant while electric charge doesn't? ...
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To what extent are quantities fundamental?

Arguably the most well-known and used system of units is the SI-system. It assigns seven units to seven ‘fundamental’ quantities (or dimensions). However, there are other possible options, such as ...
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Addition of different physical quantities

We all know the "apples and oranges" rule which says that it's meaningless to add or subtract two different quantities like apples and oranges. But the same rule doesn't hold for the multiplication ...
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3answers
191 views

What widely recognized organizations set standards used by physics?

I recently answered a question about the meaning of the word "dimension" as used in physics. In that response, I provided the definition given in the International Vocabulary of Metrology (VIM) and ...
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1answer
134 views

How to pronounce $\textrm{eV}\!/c^2$

It seems that $\textrm{eV}\!/c^2$ (and its multiples) is commonly used as the unit of mass in particle physics. For example, David Griffiths uses it quite naturally in Introduction to Elementary ...
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Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that ...
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1answer
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Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
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2answers
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Newton's Law of Graviation: Why $G$ and not e.g. $\dfrac{1}{4\pi G_0}$?

I've been wondering, in Coulomb's Law, $k_e = \dfrac{1}{4\pi\epsilon_0}$. Therefore, why do we use $G$ in Newton's Law of Gravitation? What if the constant is more like Coulomb's Law, e.g. $G = ...
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1answer
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How to interpret the appearance of time units in the units of a physical quantity?

Or phrased more abstractly, how to interpret the appearance of time dimension $[time]$ in the dimension of a physical quantity? For example, the dimension of pressure is $[mass] [length]^{-1} ...