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

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Units consistency

Does $^\circ\mathrm{C}^2$ have any physical consistency? I know that $\mathrm{K}^2$ is a valid units even if I don't know in which context it can be used. But I feel strange about $^\circ\mathrm{C}^2$ ...
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Using the boltzmann equation to find neutrino decoupling temperature

I'm an undergraduate student currently following a particle astrophysics lecture. I was reading some stuff about the neutrinos decoupling before the $e^+ e^-$ annihilations. It's possible to quickly ...
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Usage of singular or plural SI base units when written in both symbol as well as name [on hold]

I have multiple doubts related to the usage of singular or plural SI base units when written in both symbol as well as name. I have framed this question under two parts, namely, Part (a) and Part ...
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36 views

What is the use of degree in Celsius/Fahrenheit scales? [closed]

We use just 5K for 5 Kelvin BUT for Celsius and Fahrenheit, we use 5°C and 5°F respectively. Why this partiality? We do not attach the DEGREE with Kelvin scale, but we do so with Celsius and ...
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25 views

Unit definition concerning light and metre [closed]

A stupid question. I see metre is officially defined based on the speed of light: The meter is the length of the path travelled by light in vacuum during a time interval of 1 / 299 792 458 of ...
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Black Hole Entropy Calculation

I was watching "Leonard Susskind on The World As Hologram" ( youtube ). At one point he describes the way Bekenstein calculates the entropy of a black hole. Paraphrasing: Take a minimally sized black ...
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Confusion in understanding wave number

The wave number is the number of complete wave cycles in a meter. So, $$K = \frac{1m}{\lambda}$$ and also, $$K = \frac{2\pi}{\lambda}$$ so according to both of the above equation how is $$2\pi ...
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192 views

100°C = 100 K =?

I'm in first year. Our class is in lesson " Heat and Thermodynamics". While solving a numerical problem of a reversible engine he told us that 100 degree Celsius is equal to 100 kelvin. I inquired but ...
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26 views

Setting constants equal to 1 conditions

I have the following expression for the entropy of an ideal gas in a microcanonical ensemble, $$S=Nk_B\ln \left[ \frac{Ve}{N}\left(\frac{4\pi m e E}{3Nh_0^2}\right)\right] $$ Ideally I would like to ...
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351 views

Checking units for equation with degree symbol

Using the following equation: $$ U = \left(\frac{B \times L \times \sin(\theta)}{C}\right)^{1/3} $$ I can calcukate the velocity of a flow traveling down a slope. I would like to check that the ...
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86 views

Why did scientists need to invent light years?

Why did scientists need to invent light years? What's so important about having a light year? I have been learning that a light year is $9.461 \times 10^{15} \, \mathrm{m}$. My question is, why are ...
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40 views

Convert cubic feet per sec to feet per sec

Is there a way to convert cubic feet per sec to feet per sec. Or in general volumetric flow to velocity? I want to know the time taken by water to travel from point A to point B. I have the distance ...
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225 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 ...
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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: ...
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1answer
55 views

I read, some time ago about a dimensionless constant in physics [closed]

and, my terminology is probably off, but, I think I can explain with an example. Take a Newton, which can be described as a KG*Meter/Second^2 - which frankly, written that way, looks confusing to me, ...
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Complex dimensional analysis

Does complex numbers have physical dimensions? Is it sensible to talk about the dimensional analysis of $Z$ where $Z$ is the impedance of a mechanical oscillatory system? Or is it the $|Z|$ which has ...
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Units of rutherford singly differentiated cross section for secondary electron production

I have an equation that I have found in several papers which I am currently using for a project, including Waligorski (1986) and this book page 32. 4.2 BUTTS AND KATZ MODEL Butts and Katz ...
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26 views

What are the units in the heat equation?

If we write the heat equation as: $$ \frac{\partial}{\partial t}u-\alpha \nabla \cdot (\nabla u) = f $$ Then, Temperature of the material: $u: m^3\times s\rightarrow K$ Thermal diffusivity: ...
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How is it that Force = Mass $\times$ Length / Time ^2?

I understand how $F=ma$ but what I am looking for is a diagram, idiom or concept that explains how force can be explained (in a partial layman's terms) as a combination of the dimensions; Length, Mass ...
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49 views

How the torque/moment-of-force can be mathematically defined?

Given the definition of torque/moment-of-force $\mathbf F$ applied in $P$ with respect to the pole $O$ $$ \mathbf M_O=\vec{OP}\times\mathbf F $$ and given that the vectors $\vec{OP}$ and $\mathbf F$ ...
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75 views

Units in gravitational $N$ body simulations

I am trying to write a code in Python to simulate $N$ bodies interacting through gravity. In particular I am trying to see whether a system of particles with random initial positions and zero velocity ...
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Gravitational Force units

In the formula $F=mg$, does the mass $m$ needs to be in $kg$? And what is exact value of $g$? I've tried with both and didn't worked.
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Why is an Ampere an SI unit? [duplicate]

It has always annoyed me that an Ampere is an SI unit, rather than a Coulomb. Why is this the case? Was current discovered first historically? I believe that the standards were published in the 1960s, ...
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Which physical entities equal “distance times time”?

Are there useful physical quantities with dimensions of distance-time? The background for this question is a differential equation which I try to make sense of: ...
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Centripetal acceleration units

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 ...
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A query regarding constant $\frac{1}{4\pi \epsilon_{0}}$ in Coulomb's Law [duplicate]

In our physics class we were discussing about Coulomb's Law and equation for the electrostatic force between two points: $$F_{e}=\frac{Q_{1}Q_{2}}{4\pi \epsilon_0 r^2}$$ From the equation a query ...
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27 views

Is there a way to convert CFM (rate of air moved) to kilograms of lift generated?

Is there a way to convert CFM as in a rate of volume of air moved to kilograms of lift generated?
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113 views

Is there a commonly used unit of measure (other than temperature units) that is not absolute? [closed]

I live in a country where we use Degree-Celsius(°C) to measure the temperature. Sometimes from one day to the other, the temperature rises from 10°C to 20°C and I hear people say, "Wow! Today is twice ...
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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 ...
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Do I need to convert units to be compatible with constants?

I want to calculate the wavelength of radiation given its energy. I know I need to use $E=h f$ and $f = c / \lambda$. All I'm given is $E = 20 \text{ keV}$, now my true question is: Do I use $E = ...
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How to find gravitational acceleration given $k$ in a power function

I have a problem that has been bugging me for a week, and I can't figure it out. We know the power function: $$ y=kx^n $$ I also have a set of data: I took the natural log of both of these data ...
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Neutrino decoupling and units

I have a problem that states: In the early Universe, neutrinos can be created and destroyed by the process: \begin{equation} \nu \bar{\nu} \leftrightarrow e^{+}e^{-} \end{equation} The thermally ...
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Proper way to write the units to indicate that they include an offset?

Past a certain point of complexity, I get rather confused with physical units, so I am asking a physicist for help. I have a code that represents temperature, with a resolution of [0.5 °C], whose ...
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45 views

What unit would the answer be in?

So I have used this formula: $$W= PV_1 \times \ln\frac{V_2}{V_1}$$ and I have converted my values to cubic meters and pascals. So Work Done, $W$, what would be the unit for that answer? I already ...
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Ultimate Planck Frequency [closed]

Is there an upper limit to the Planck Frequency? Does it simply depend upon the inverse of the Planck Time unit?
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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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101 views

Is it possible to prove that units can be manipulated algebraically?

With expressions such as $$4\ \mathrm{\frac{m}{s}} \times 2\ \mathrm{kg} = 8\ \mathrm{\frac{m}{s}} \times 1\ \mathrm{kg}$$ We can justify that a $2\ \mathrm{kg}$ mass moving at $4\ \mathrm{m/s}$ has ...
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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 ...
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70 views

In the expresion $4\sin (\theta) \frac{d \theta}{d t}=\frac{dy}{dt}$ Which is the correct unit of $\theta$ ¿ radian or degrees? [closed]

If I change units of an angle for radians to degrees in the next expresion $$4\sin (\theta) \frac{d \theta}{d t}=\frac{dy}{dt}$$ the value of $$\frac{dy}{dt}$$ changes. For example at a rate of ...
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What really generates time evolution?

A fundamental principle of quantum mechanics, as far as I can tell, states that the Hamiltonian generates time evolution. A common result about generators are the following: let $\mathrm T$ be the ...
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686 views

Do the probability density and the probability current density have a unit

I could not find what is the probability density and the probability current density of one-dimensional Schrödinger equation units?
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67 views

Spectral irradiance units conversion

I have a table of data containing irradiance of light at different wavelengths. This is how it looks like for 300.5 nm: Wavelength, nm: 300.5 Wavelength, $\mu$m: 0.3005 W/m$^2$/$\mu$m: 403 ...
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405 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? ...
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How to understand/derive Eq 5.5 in Geiner's Quantum Mechanics - An Introduction?

Geiner's Quantum Mechanics - An Introduction has an unnumbered equation above Eq. 6 in section 2.4 discussing density -- not sure if it is energy density -- of radiation: ... $$dE/dV = E/V =a ...
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Natural units in a parallel universe [closed]

Taking ispiration from this question units and nature . The natural Plank units set the gravitational costant $G$, the planck costant $\hbar$, the speed of light $c$, the Boltzmann costant $k_B$ and ...
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constant $c$ in Lorentz force

I met some of examples of force in studying classical dynamics, and Lorentz force was represented as $$ \mathbf{F}=\frac{q}{c} \mathbf{\dot{r}} \times \mathbf{B} $$ I've searched for meaning of $c$, ...
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Proportionality and units

This might be very easy, but I'm not 100% sure how it's done. Lets say I have this equation: $$R = R_{0} \cdot \left[1 - \frac{P_{0}R_{0}}{GM_{0}\rho_{0}}\right]^{-1},$$ where I know $P_{0}$, ...
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Reconciling Units in Classical System Analogies: Why Does Torque Have Units of Energy?

In classical physics we often cast an analogy between translational and rotational systems Force < > Torque Energy < > Rotational Energy Momentum < > Angular Momentum and considering SI ...
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Operations on physical quantities [closed]

I know what quantities like meter and second are, they are a certain quantity of one-dimensional space and a certain duration of time respectively. And I know what a measurement of a quantity using a ...
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What does the $c$ in $eV/c^2$ stand for?

I have been wondering(also searching) for what does the $c$ in eV/$c^2$ stand for? (For example, mass of the electron is $0.511 \, \text{MeV}/c^2$.) I have read that this unit has been derived from ...