Tagged Questions

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

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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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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 $L = 1 km$. $\log L = \log km$ ...
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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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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 ...
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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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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 ...
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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 ...
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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 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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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 ...
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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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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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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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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 ...
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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" ...
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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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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 ...
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What in nature causes Newton's gravitation constant to have its given value?

Does the value of Newton's universal gravitational constant $G$ remain a mystery? Why does it have the value that it has?
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When can the constant of proportionality in an eq be set equal to 1 and when not? [duplicate]

In $F=kma$, $k=1$ but in $F=kx$, $k$ is not equal to 1?So what are the conditions for the constant of proportionality to be set 1?
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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, ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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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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 $c=1$...
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How can I convert $$W m^{-2} sr^{-1} nmm^{-1}$$ to $$W m^{-2} nm^{-1}$$ I have the following matlab code to illustrate the spectral energy distribution of solar radiation: ...
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Why are significant figure rules in Multiplication/Division different than in Addition/Subtraction?

I've never understood specifically why this is. Here's what I mean. In Addition/Subtraction, what matters are the digits after the decimal point. So for example: 1.689 + 4.3 = ...
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Why is the absolute zero -273.15ºC?

I can't find an answer of why the lowest temperature is -273.15ÂșC. Is it deduced theoretically or is it experimental? An explanation is that when any gas volume tends to zero, the temperature will be ...
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Base quantities and charges

Is there an unit of color charge? I haven't found it, so I suppose that it doesn't exist, if this is right, why? Isn't it supposed that every measurable quantity can be expressed in terms of base ...
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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 ...
I perform some basic calculation for circular motion. Formulas we get from school are: $v$ - Linear speed with the units m/s $r$ - Radius of curve in meters $\omega$ - Angular speed with the units ...