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Questions tagged [units]

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

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172
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16answers
16k views

Are units of angle really dimensionless?

I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've ...
90
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3answers
20k views

Why was carbon-12 chosen for the atomic mass unit?

The atomic mass unit is defined as 1/12th the mass of a carbon-12 atom. Was there any physical reason for such a definition? Were they trying to include electrons in the atomic mass unit? Why not ...
82
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6answers
14k views

Why is it “bad taste” to have a dimensional quantity in the argument of a logarithm or exponential function?

I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although ...
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9answers
17k views

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 ...
67
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10answers
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Should zero be followed by units? [duplicate]

Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some ...
59
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2answers
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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 ...
51
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11answers
33k 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 $L = 1 \:\mathrm{km}$. $\log L = \...
51
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5answers
6k views

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 ...
50
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6answers
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Why can fuel economy be measured in square meters? [closed]

With help from XKCD, which says Miles are units of length, and gallons are volume — which is $\text{length}^3$. So $\text{gallons}/\text{mile}$ is $\frac{\text{length}^3}{\text{length}}$. That's ...
47
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10answers
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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. Work & Energy are also measured in Newton ...
39
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4answers
10k views

Can units be plural? [duplicate]

I was in a conversation with my senior engineer where he kept on insisting that we can use plural when we write down any unit. I argued that it is not the 'common' practice or even throughout my whole ...
37
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6answers
9k views

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 ...
34
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10answers
5k views

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, ...
32
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8answers
22k views

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" ...
32
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2answers
19k views

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 ...
31
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3answers
3k views

What is a “decade” as a unit of measure (ex. a decade of the EM spectrum)?

Reading through papers and online sources about radio galaxies, I kept stumbling across a term--a "decade" of the electromagnetic spectrum. Radio galaxy emission encompasses "11 decades of the EM ...
30
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12answers
13k views

Do all equations have identical units on the left- and right-hand sides?

Do all equations have $$\text{left hand side unit} = \text{right hand side unit}$$ for example, $$\text{velocity (m/s)} = \text{distance (m) / time (s)},$$ or is there an equation that has different ...
30
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5answers
11k views

Why do we use the electron volt?

Why do we use the electron volt? Why did it come to be the electron volt and not, say, just a prefix of the joule, like the nanojoule? Does the electron volt represent anything particular as far as ...
30
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5answers
6k views

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 ...
29
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11answers
58k views

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 ...
29
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2answers
3k views

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?
28
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3answers
21k views

Why does the metric system use “kilogram” as a base 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 ...
26
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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 = \int_{-...
25
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9answers
9k views

How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot 4\...
25
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4answers
1k views

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

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 equations be expressed so neatly ...
24
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6answers
4k views

Why is the meter considered a basic SI unit if its definition depends on the second?

The metre is the length of the path travelled by light in vacuum during a time interval of 1  ⁄ 299792458 of a second. – 17th CGPM (1983, Resolution 1, CR, 97), source The meter (or metre) is ...
23
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3answers
5k views

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?
23
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3answers
2k views

Is $0\,\mathrm{m}$ dimensionless?

Is $0 \, \mathrm m = 0 \, \mathrm s = 0 \,\mathrm {kg} = 0$? How do we define $[0 \, \mathrm m]$? I once was given an assignment where I was asked to deduce and write down some physical quantity. It ...
19
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2answers
4k views

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? ...
17
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3answers
2k 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 ...
17
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4answers
4k views

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 ...
16
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7answers
5k views

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 ...
16
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7answers
10k views

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 ...
15
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5answers
3k views

Why does a calculation to count objects covering a certain area seem to give nonsensical units?

Suppose you want to estimate the number of atoms in a rectangular sheet of graphene. You might estimate the sheet to have $10^{7}$ atoms along one edge and $2*10^{7}$ atoms along the other edge. ...
14
votes
7answers
3k views

Why are work and energy considered different in physics when the units are the same?

There is a question that explains work and energy on stack exchange but I did not see this aspect of my problem. Please just point me to my error and to the correct answer that I missed. What I am ...
14
votes
2answers
8k views

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, ...
14
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4answers
3k views

Why is the mol a fundamental physical quantity? [duplicate]

I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity. A physical quantity is any quantity ...
14
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6answers
1k views

What examples are there of unrelated physical quantities measured in the same units? [closed]

Torque and energy have the same dimensionality, and so logically are measured in the same units (joules). However, it seems more natural to call the unit for the former a “newton-metre”, because ...
14
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3answers
7k 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 $G$ ...
14
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5answers
2k 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 ...
14
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1answer
905 views

What's the difference between a realization, a representation and an implementation in metrology?

In a recent answer, a metrologist casually used the terms 'realization' and 'implementation' of an SI unit as if they were different, which looks very strange to the untrained eye. Some further ...
14
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1answer
1k views

What is a base unit in the new SI, and why is the ampere one of them?

One question that comes up pretty much always in introductory electromagnetism courses is Why the base unit of electrical measurements is the ampere and not the coulomb, and the usual answer is that ...
13
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2answers
3k views

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, ...
13
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2answers
2k views

Why isn't temperature measured in joules per mole (J/mol)? [duplicate]

Temperature is the average kinetic energy of all the molecules in a system. Thus \begin{align} T &= \frac{1}{N}\sum \frac{1}{2} m v^2 \\[6pt] &= \sum \frac{E_\text{single particle}}{n} \cdot ...
13
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3answers
9k 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 ...
12
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5answers
3k views

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?
11
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10answers
3k views

Is it mathematically wrong to use units instead of words/parameters/names in equations?

In equations that have quantities with physical dimension. Example: $\mathrm{Force} = (\mathrm{mass})(\mathrm{acceleration})$ or $F=ma$ I know that we use that (mass, force...) to help what we ...
11
votes
6answers
5k views

Is speed of light and sound rational or irrational in nature?

Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ? I'm talking about ...
11
votes
3answers
21k views

273 + degree Celsius = Kelvin. Why 273?

Temperature conversion: $$273 + \text{degree Celsius} = \text{Kelvin}$$ 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 ...
11
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4answers
3k 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: ...