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

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Are there any scales other than temperature that have different zero points? [closed]

For most physical measurements, zero is the same regardless of the units used for the measure: $0 \mathrm{mi} = 0 \mathrm{km}$ $0 \mathrm{s} = 0 \mathrm{hr}$ but for absolute temperatures, ...
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4answers
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Fundamental question about dimensional analysis

Let me admit beforehand that this is quite possibly a very stupid question. I was also uncertain of where to post this question, as it doesn't fit cleanly into either physics or math stackexchange. ...
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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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11answers
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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 ...
22
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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 ...
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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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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 ...
20
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1answer
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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 ...
19
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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" ...
17
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3answers
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What is the length of 1 second in meters

If time is treated as a fourth dimension of spacetime, what is relation between length and time units? Or in other words, how can I convert time units to length units, for instance seconds to meters? ...
14
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3answers
948 views

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 ...
14
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4answers
716 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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4answers
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Is the Avogadro's constant equal to one?

Question: Is the Avogadro's constant equal to one? I was tasked with creating a presentation on Avogadro's work, and this is the first time I actually got introduced to the ...
12
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2answers
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Why are magnetic fields so much weaker than electric?

In EM radiation, the magnetic field is $ 3*10^8$ times smaller than the electric field, but is it valid to say it's "weaker". These fields have different units, so I don't think you can compare them, ...
11
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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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5answers
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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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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 ...
10
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4answers
580 views

How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...
9
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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 ...
9
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3answers
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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? ...
9
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2answers
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What are the units or dimensions of the Dirac delta function?

In three dimensions, the Dirac delta function $\delta^3 (\textbf{r}) = \delta(x) \delta(y) \delta(z)$ is defined by the volume integral: $$\int_{\text{all space}} \delta^3 (\textbf{r}) \, dV = ...
9
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1answer
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How is a standard unit divided into equally smaller or fractional units physically/experimentally?

Consider the standard unit of length: meter. How was it divided into decimeter, centimeter, millimeter, etc. when there were no shorter lengths than the standard? What is the physical/experimental ...
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5answers
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Is 'amp' a technically invalid term?

I've been told to use the term ampere in exams and class (I'm in high school), instead of amp as it's not a valid unit, although I've been using the amp for years along with all of my friends who do ...
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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 ...
8
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863 views

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, ...
8
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4answers
346 views

Physical representation of volume to surface area

I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume ...
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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. ...
7
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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 ...
7
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2answers
499 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, ...
7
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5answers
401 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 ...
7
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4answers
898 views

What's the dimensionality of a solid angle?

I haven't seen this explained clearly anywhere. Solid angles are described usually as a fraction of the surface area of a unit sphere, similar to how angles are the fraction of the circumference of a ...
7
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2answers
898 views

Having trouble weighing the sun

So I gather the way you (and Vera Rubin) calculate a galaxy's mass is by measuring a star's orbital velocity $v$ and its distance $R$ from the galactic center, and then plugging them into this ...
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Whats the range of dimension exponents in the SI Units system?

I am working on a software library for Units of Measure. To represent dimensions, I need to know the required range of exponents for each of the seven base units (precisely, I need to know the ...
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477 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 ...
6
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4answers
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What exactly is a mole?

I have some trouble understanding exactly what a mole represents. As I understand, one unit mole is 1/12 of the mass of an atom of carbon-12 (thus it is the mass of one nucleon?). What is a mole, ...
6
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4answers
501 views

Is there a quantity measured in kilogram seconds?

I'm trying to get a full grasp on the relationship between many of the units that are used in kinetic physics. I've found that it is possible to make a venn-diagram that shows the factors of many of ...
6
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1answer
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“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? ...
6
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3answers
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Einstein tensor in Friedmann equations : where is the missing $c^2$?

I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere. In all the following $\rho$ ...
6
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1answer
364 views

What are units actually?

This question is about the concept of units in physics. Firstly - do units have a formal mathematical definition? How are they different from pure numbers? Are pure numbers defined to be ratios of ...
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2answers
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Why metric system uses kilogram as a basic SI unit?

SI system uses all (that I know) measurement basic units as 1 (single) instance: meter, second, ampere, etc, except the KILOgram. It already defined with 1000 multiplier (kilo). It prevents from ...
6
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3answers
213 views

Units of a discrete Fourier transform

Normally a Fourier transform (FT) of a function of one variable is defined as $$f_k=\int^\infty_{-\infty}f(x)\exp\left(-2\pi i k x\right) dx.$$ This means that $f_k$ gets the units of $f$ times the ...
5
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8answers
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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 ...
5
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3answers
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Why is 1 AU the distance between the Sun and the Earth?

Why 1 AU is defined as the distance between the Sun and the Earth? (approximately if you like to be precise) An astronomical unit (abbreviated as AU, au, a.u., or ua) is a unit of length ...
5
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2answers
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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 $G$ ...
5
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2answers
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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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How much is if my internet provider says “we have increased your WiFi connection by 2 decibels”?

I understand the definition of decibel as a logarithmic unit for intensity of anything. I just cannot imagine its "actual size" when comes to the wireless connection. Can you provide something ...
5
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What is a “measure equation” as mentioned by this TeX Users Group guide?

In this TeX Users Group (TUG) document, Typesetting mathematics for science and technology according to ISO 31/XI by Claudio Beccari, the author makes various typesetting recommendations including: ...
5
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Units inside a logarithm

I have troubles understanding a seemingly simple integral in a physical context. Take a look at $\int_{V_1}^{V_2} \frac{\mathrm{d}V}{V}$ which appears in isothermal expansions (V being the volume of a ...
5
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2answers
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In what order should unit symbols appear?

I am trying to represent the result of a dimensional analysis calculation and I can't find an official document that lists the order that unit symbols should appear. For example, when I google ...
5
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Is there a conveniently small unit of volume for talking about molecules?

When discussing energy transformations on the molecular scale, we usually use electronvolts as the energy unit. This is handy because chemical bond energies are a few electronvolts in magnitude. I ...