Units are standards of measurement used for different types of quantities.
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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" ...
16
votes
6answers
1k 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 ...
16
votes
9answers
1k 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 ...
15
votes
3answers
740 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?
...
14
votes
3answers
1k views
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.
...
13
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9answers
3k 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 ...
12
votes
6answers
2k views
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 ...
12
votes
4answers
750 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 ...
8
votes
3answers
548 views
Understanding counterintuitive units like s^2
One of the things I never understood but was too afraid to ask is this: how should I think of things like kg/s^2. What exactly is a square second? Square foot makes sense to me because I can see it, ...
8
votes
4answers
488 views
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 constant $k$ ...
8
votes
2answers
920 views
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 ...
7
votes
5answers
660 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 ...
7
votes
4answers
380 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 ...
7
votes
5answers
134 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 ...
6
votes
5answers
876 views
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. ...
6
votes
5answers
472 views
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 ...
5
votes
7answers
695 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 ...
5
votes
2answers
198 views
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 $\rho$ ...
4
votes
4answers
1k views
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, ...
4
votes
3answers
475 views
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 ...
4
votes
7answers
358 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 ...
4
votes
2answers
304 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 $G$ ...
4
votes
10answers
882 views
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 ...
4
votes
3answers
177 views
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:
...
4
votes
1answer
273 views
$E^2 = (mc^2)^2 + (pc)^2$: What units are used to measure $E$, $m$, $c$ and $p$?
\begin{equation}
E^2 = (mc^2)^2 + (pc)^2
\end{equation}
If I am using this equation to figure out the energy of something, what units would I use? Would it be the metric system? I.e. kilograms ...
4
votes
1answer
676 views
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 = ...
4
votes
2answers
153 views
The “official” mass of the sun as unit?
I'm searching for the "official" mass of the sun as a unit in astrophysics.
The mass of the sun can be calculated by:
$M_{\odot}=\frac{4\pi^2\times(1 \ \text{ua})^3}{G\times(1\ \text{year})^2}$
So ...
3
votes
5answers
512 views
Does the unit of a quantity change if you take square root of it?
For example, I have a mass, m = 0.1kg and I square root it, giving me m = 0.316 (3s.f.) does the unit still stay as kg, or does it change?
3
votes
1answer
151 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 ...
3
votes
3answers
393 views
$\hbar$, the angular momentum and the action
Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
3
votes
1answer
196 views
Do the trigonometric functions preserve units?
I saw an exercise where you had to calculate the units of $C_i, i=1,2$ from an equation like this:
$v^2=2\cdot C_1x$ and
$x=C_1\cdot \cos(C_2\cdot t)$
where
$x$ means meters,
$t$ means seconds ...
3
votes
1answer
104 views
Official definition of astronomical units
As it is relatively easy to find an official value for a large number of physical constants, (thanks to CODATA), it is not so easy for some units widely used in astronomy (Wikipedia, Google and IAU ...
3
votes
1answer
48 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?
3
votes
2answers
538 views
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 ...
3
votes
1answer
1k views
How does the Fourier Transform invert units?
I don't really understand how units work under operations like derivation and integration. In particular, I am interested in understanding how the Fourier transform gives inverse units (i.e. time ...
3
votes
3answers
223 views
Physical interpretation of describing mass in units of length
I'm working in Taylor and Wheeler's "Exploring Black Holes" and on p.2-14 they use two honorary constants: Newton's constant divided by the speed of light squared e.g. $G/c^2$ as a term to convert ...
3
votes
2answers
509 views
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
votes
3answers
323 views
How do Temperature Scales work?
How exactly do temperature scales work?
If my understanding is correct, the Celsius scale has two fixed points: (definitions of temperature irrespective of scale)
1. The freezing point of pure water ...
3
votes
1answer
156 views
Gravity and Planck scale
What is the connection between Planck's constant and gravity? Why is the Planck scale the natural scale for quantum gravity? I would have though the scale would be related to G, not h.
3
votes
3answers
105 views
What is the missing proportionality constant in the magnetic levitation formula?
The formula for magnetic levitation is
$$ B \frac{dB}{dz} = \frac{ \rho g }{\chi} $$
but as always, I have a hard time figuring the units in SI. The left hand side is $\mathrm{T^2 /m}$, while $\chi$ ...
3
votes
1answer
78 views
Units for physical constants
Someone told me that units for $G$ and $\epsilon_0$ (gravitational constant and Coulomb's constant) are placed there simply to make equations work dimensionally and that there is no real physical ...
3
votes
1answer
106 views
Help on unit conversion problem
This is a problem from school. I will show my attempt.
The question:
"The gas constant for dry air R is 287 $\frac{m^2}{s^2*K}$. Assuming the temperature is 330 K and the pressure is 1050 hPa, what ...
3
votes
1answer
172 views
Question about units in Lagrangian dynamics (inertia matrix)
I have a 3 degree of freedom system and my equation of motion is like this:
$$M(q)q_{dd} + C(q,q_d)q_d+G(q)~=~0$$
$M(q)$: inertia matrix
$C(q,q_d)$: Coriolis-centrifugal matrix
$G(q)$: potential ...
2
votes
4answers
217 views
Are circularly defined {velocity, distance, and time} a problem in physics?
In order to measure velocity, one needs a calibrated measuring stick and clock. But in order to calibrate a measuring stick you need a calibrated clock and velocity. And in order to calibrate a clock ...
2
votes
3answers
165 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 ...
2
votes
2answers
487 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?
2
votes
6answers
344 views
Confused about unit of kilowatt hours
So I am a little confused on how to deal with the Kilowatt hours unit of power, I have only ever used Kilowatts and I have to design a residential fuel cell used as a backup generator for one day.
...
2
votes
1answer
233 views
Conversion from natural units to SI
I got questions about converting units from natural system of units to SI.
To be exact, I'm solving the problem in Heisenber interpretation of quantum mechanics, and I'm using Heisenberg equation of ...
2
votes
2answers
957 views
Decibel level addition of multiple noise sources
If I have four computer fans of which each is said to run at 46 dB, and they run close to each other, how loud is the whole system?
I somehow recall from my physics course that 10 decibel ...
2
votes
2answers
44 views
What are the units of these virial coefficients?
I'm reading some papers for calculating the vapor pressure of alkali metals as a function of temperature, and I've come across some familiar-looking virial expansions, but when I tried to work out the ...
