Questions tagged [units]

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

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60
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2answers
3k 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 ...
19
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2answers
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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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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 $L = 1 \:\mathrm{km}$. $\log L = \...
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3answers
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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 ...
51
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5answers
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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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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 ...
29
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11answers
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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 ...
16
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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 ...
14
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1answer
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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 ...
25
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4answers
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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 ...
32
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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 ...
14
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3answers
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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 ...
171
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16answers
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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 ...
38
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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 ...
17
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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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6answers
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How to derive $E=mc^{2}$?

Is there some way to derive $E=mc^{2}$? I can understand that energy in something is proportional to its mass, but the $c^{2}$ part. I have no idea. It seems like the way the units are going it would ...
15
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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 ...
9
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7answers
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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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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 ...
3
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2answers
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What is the real interpretation of Planck's constant and what are its origins?

In the physics texts I have read and from other online information, I gather that Planck's constant is the quantum of action or that it is a constant specifying the ratio of the energy of a particle ...
82
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6answers
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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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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 ...
14
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4answers
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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 $G$ ...
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2answers
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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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2answers
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How can Planck units be consistent with conflicting dimensions of mass?

I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = \...
33
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8answers
23k 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" ...
14
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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, ...
6
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3answers
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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 ...
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5answers
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What is the significance of Planck force?

I have been curious to find what could be the significance of Planck force? It is calculated by the formula $c^4/G = 1.21031359\times 10^{44} \, \mathrm{N}$, where $c$ is the speed of light and $G$ is ...
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6answers
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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 ...
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3answers
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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 ...
6
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4answers
949 views

Why are electrical units (specifically, electrical current) considered a base unit?

Note: this is NOT a question why current is the base unit as opposed to charge—that’s because measuring $1 \ \mathrm{ A }$ through a wire is easier to measure in a lab than is $1 \ \mathrm{ C }$ in ...
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1answer
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Degree celsius vs. Celsius degree

While reading my copy of "Resnick and Halliday", I noticed that the book has made a distinction b/w the terms " degree celsius" and "celsius degree". When I googled this, I was able to find only one ...
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2answers
562 views

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 = \dfrac{...
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3answers
538 views

Why did Einstein took speed of light unit or constant in his equation of relativity?

We can find that no object can have speed more than light from Einstein's equation of relativity because if anything have speed more than light then we get -ve value within square root. But why did ...
90
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3answers
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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 ...
29
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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_{-...
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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 ...
14
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7answers
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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 ...
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6answers
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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 ...
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2answers
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When can two quantities be added together?

Whenever two things are to be added together, one typically needs to check whether this actually makes sense, and an addition is said to make sense, in principle, when the units match up. Yet, ...
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9answers
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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 $\mathrm{m\ s^{-1}}$ to $\mathrm{km\ s^{-1}}$, but why can we just delete the units altogether? My question is: what exactly are we doing ...
30
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5answers
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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 ...
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4answers
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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 ...
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3answers
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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 ...
3
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1answer
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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 ...
3
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2answers
2k views

Fundamental units

Is it right that all units in physics can be defined in terms of only mass, length and time? Why is it so? Is there some principle that explains it or is it just observational fact?
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4answers
980 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 ...
6
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3answers
460 views

Are there Planck units for weak or strong “charge”, similar to the electromagnetic Planck charge $\sqrt{4~\pi~\epsilon_0~\hbar~c}~$?

Are there Planck units for "charge" of weak or strong interaction, similar to the Planck unit of electromagnetic charge: $\sqrt{4~\pi~\epsilon_0~\hbar~c}$ ? Are there perhaps direct substitutes, ...
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3answers
2k views

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 ...