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Questions tagged [units]

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

The most prevalent system of units is the SI (Système international d'unités). It consists of seven base units: meter (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), candela (luminous intensity), and mole (amount of substance). Units for other quantities are derived from these, for example velocity is $\text{m/s}$ or meter-per-second.

Units need not make any physical sense unless rearranged in the correct manner. For example, writing surface tension as $\mathrm{\frac{kg}{s^2\cdot m^2}}$ need not make any intuitive sense. If it is rewritten as $\mathrm{N \cdot m^{-1}}$, then we can clearly see that it has to do with force per unit length.

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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 been writing a c++ dimensional analysis library…
Nicolas Holthaus
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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 define the amu as the mass of one proton or neutron…
Dieblitzen
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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 I suppose it would be weird to raise a…
sangstar
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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 temperature, the candela for luminous intensity,…
Wais Kamal
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Should zero be followed by units?

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 teachers were saying that, yes, it should be while…
Vidyanshu Mishra
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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 fundamental constants of nature than were possible when…
Emilio Pisanty
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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 meters which are Joules. However, torque isn't a measure…
General Stubbs
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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 for that matter, with units at all) together; these…
Jubilee
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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 $L = 1 \:\mathrm{km}$. $\log L = \log \mathrm{km}$ It seems that the unit of $\log…
Statec
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Why can fuel economy be measured in square meters?

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 just $\text{length}^2$. I recently realised that the…
AvahW
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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 times $\frac{T}{2}$. Why do we need separate units…
jcai
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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 varies from source to source; there are a few…
Emilio Pisanty
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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_{-\infty}^{\infty} \int_{-\infty}^{\infty}…
Andrew
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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" on several columns...and I'm quite surprised I…
Ben
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Can units be plural?

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 academic career (unfortunately) I haven't found…
Ahmed
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