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

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convert units for spectral irradiance

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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Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that ...
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Planck time, distance, mass? Why do we take those values?

Say we want to make an educated guess for critical values of time, distance and mass, where quantum gravity effects are supposed to be non-negligible. These values are given the prefix "Planck-". Now, ...
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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 ...
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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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Units and Dimensions - Use of proportionality constant

In units and dimensions we learn about Establishing a Formula : (example) : to establish a relationship between T (Time Period) , m (Mass) , l (length of the string) and g(acc. due to gravity) - ...
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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. ...
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607 views

What really is Planck's constant and what are its origins?

In the physics texts I have read and other info online, they says Planck's constant is the quantum of action or that it is a constant of the ratio of the energy of a particle to its frequency. Im ...
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140 views

How to interpret the appearance of time units in the units of a physical quantity?

Or phrased more abstractly, how to interpret the appearance of time dimension $[time]$ in the dimension of a physical quantity? For example, the dimension of pressure is $[mass] [length]^{-1} ...
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730 views

Question Concerning Dimensional Analysis

In the first lecture of MIT's Classical Mechanics Professor Lewin talks about Dimensional Analysis.He talks about an apple being dropped from a certain height can be quantitatively expressed as the ...
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Is dimensional analysis always sufficient to establish equivalence of quantities?

In dealing with the Biot-Savart law, it was argued that $$ q\frac{d\vec{s}}{dt}\equiv Id\vec{s} $$ using the fact that the units are equal. Does this kind of argument always work? It seems too ...
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What is a proportionality constant? (Planck's constant)

I understand that Planck's constant is essentially the ratio between the energy of a photon and its frequency. There are 2 things that im trying to verify: isn't the number that Planck's constant ...
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Understanding units manipulation (speed of falling coconut after 20m)

When I was on holidays, I was told a story about how someone passing under a palmtree and almost got a coconut fall on his head. Given that these palmtrees where about $20m$ high, we wondered at what ...
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Why metric system uses kilogram as a basic SI unit?

SI system uses all (that I know) measurement basic units as 1 (single) instance: meter, second, ampere, etc, except the KILOgram. It already defined with 1000 multiplier (kilo). It prevents from ...
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267 views

If we are using [eV] as a unit for energy, what, then, should the unit for mass and distance be?

This seems obvious but it is confusing since I know that in MKS (i.e. SI) system, we use Joule with Meter with KG. But if we're using electron volt (1.6e-19 J) for energy, should we change the mass ...
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447 views

Why is the candela dimension J, not W?

According to the table at the bottom of the Wikipedia page for the candela, the dimension for candelas is J (joules). Why is this not W (watts)? The luminous intensity for light of a particular ...
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315 views

Force and Natural Units

Today in my Physics lecture I suddenly thought of something. We all know that gravitational force is proportional to the two masses and inversely proportional to the square of the distance between ...
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How to choose the right units to compute the phase space volume in classical statistical mechanics?

Without the natural unit $\hbar$, why doesn't it seem to be a problem for Statistical Physics to define $$S=k_B\ log(\Omega)\ ?$$ If $\Omega$ is given in one unit system and I switch to other units ...
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Is there a difference between Hertz and 'frames per second'?

It's not uncommon that the term 'frames per second' (sometimes abbreviated as fps or FPS) is associated with, or even equated to, the unit Hertz (Hz). I'm not exactly sure how these two concepts ...
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42 views

Differences between 3 apples and 3 kg of apples according to base units

7 base units are defined in physics and other units are derived from these units. When we say "3 kg of apples", we mention its mass and mass is a base unit. But for "3 apples", what is its unit? Is ...
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Does the unit of Inertia include radians? [duplicate]

The unit for angular acceleration $\alpha$ is: $$\mathrm{rad/s^2}$$ The unit for torque is $\mathrm{Nm}$: $$\mathrm{kg\ m^2/s^2}$$ And their relationship with Inertia is: $$I = \tau/\alpha$$ So ...
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Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi ...
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When “weight” of an object is listed, is it really the mass or the weight?

I Have read an earlier post regarding this, but the answer wasn't perfect enough or I didn't understand so! Let me put it to clear, I know difference between weight and mass. Also I know the ...
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303 views

How do the units for angular velocity come out of $\omega = \sqrt{k/m}$?

I'm confused about an exercise of a book. I understand that the units for angular velocity is $\text{rad/s}$; but I don't understand, how can I get it from the relation $\omega=\sqrt{k/m}$. Solving ...
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Is there a name for a quantity that represents (volumetric) flow per unit of mass?

In a lot of medical literature about blood flow in the brain, researchers denote the amount of volumetric blood flow that passes through a certain amount of brain tissue as "cerebral blood flow". ...
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Why is the unit of hydraulic impedance/resistance kilogram per second and hypermeter?

I'm trying to figure out the unit of impedance in the hydraulic analogy of electronic networks. Assuming $$Z=\frac{P}{Q},$$ with $P$ as pressure difference, $Q$ as volumetric flow rate and $Z$ as ...
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59 views

Is there a standard reference where entropy is set equal to zero in property tables?

For practical considerations, it seems that entropy is only meaningful as a difference between states, like $\Delta s$ going from state A to state B. For an ideal gas, for instance, standard formulas ...
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69 views

Has a system of natural units been designed for human-like scales?

A long time ago I was thinking about how the Imperial system of measurements is arbitrary and annoying, and I decided to design the best system of units ever (I wasn't very old then). I worked on this ...
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52 views

Why do we take the value of the constant in Coulomb's law as $\frac{1}{4\pi\varepsilon_0}$? [duplicate]

Why do we take the value of the constant in Coulomb's law as $\frac{1}{4\pi\varepsilon_0}$?
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Units and missing constants in quintessence expressions?

In cosmology, quintessence is an alternative to the cosmological constant. In this approach (described here), we consider a scalar field $\phi$ and its self-interacting potential $V\left(\phi\right)$ ...
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Different factors of $4\pi$ and $\epsilon_0$ in Poisson equation [duplicate]

Some authors claim the Poisson equation is $$\nabla^2 \psi = -\dfrac{\rho}{\epsilon\epsilon_0}$$ (e.g. Wikipedia) whereas other ones (e.g. Andelmann) claim it is $$\nabla^2 \psi = ...
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Why can't the units of work and torque be interchanged? [duplicate]

When I'm studying about work and torque, I found that their unit are the same. But, why don't we use Joule (unit of work) instead of Newton-meter (unit of torque)? Since $\mathrm{1\ Joule = 1\ Nm}$, ...
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Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
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Is dimensional analysis used outside fluid mechanics and transport phenomena?

Most dimensionless numbers (at least the ones easily found) used for dimensional analysis are about fluid dynamics, or transport phenomena, convection and heat transfer - arguably also sort of fluid ...
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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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195 views

Difference between nautical and terrestrial miles

Does someone know the historical reason behind the difference in physical units between nautical and terrestrial miles?
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How to check units?

I've got: $Q=\frac{Er^2}{k}$ how to check the units? I start with $\left[\frac{\text V}{\text m} \, \text m^2\right]$, tried replacing $[ \text V ]$ with $\left[ \frac{\text J}{\text C} \right]$, but ...
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How could the unit of a constant be unit of tension $N^{-1}$?

From my pervious Question:What are the units of the quantities in the Einstein field equation? i noticed that the unit of this constant $\frac {G}{c^4}$ is the unit of tenstion $$\frac ...
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Which is the most fundamental constant between the Planck constant $h$ and the reduced Planck constant $\hbar$?

This question is related to Planck units (also called natural units, absolute units or God's units). I'm wondering which constant is the most fundamental and should be normalized to 1. I would like as ...
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141 views

Boltzmann constant--why units aren't joules per degree PER MOLECULE

I didn't think the information I looked at did a very good job of explaining the Boltzmann Constant, kB, but once I did this next simple calculation, it seemed clear that what I didn't understand were ...
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2 dimensional Coulomb's law equation

We can notice that in the Coulomb's law equation, $$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$ $4\pi r^2$ factor in the denominator expresses directly ...
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Aggregating daily readings with units of parts per million

I have a series of daily readings (NOx emissions) measured in parts per million. I need to aggregate the daily readings into a monthly measure. Clearly a sum operation will be incorrect (parts per ...
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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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Temperature in CGS (Gaussian) units

I've been struggling with conversion from Gaussian to SI units for sometime, trying to figure out how derived units in CGS (current, charge etc) relate to the SI units. But I couldn't find any ...
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Showing that position times momentum and energy times time have the same dimensions

I've been asked to show that both the position-momentum uncertainty principle and the energy-time uncertainty principle have the same units. I've never see a question of this type, so am I allowed to ...
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Why is the Coulomb taken as the unit positve test charge, though $1 C$ charge is a high value? [closed]

Why is the Coulomb taken as the unit positve charge, though $1 C$ charge is a high value?
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double of temperature

I'm not a physicist, but I was having a discussion with a friend and I could not convince her about the main point. I asked her: "If I am in a place which temperature is 10ºC and she is in a place ...
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Factors of $c$ in the Hamiltonian for a charged particle in electromagnetic field

I've been looking for the Hamiltonian of a charged particle in an electromagnetic field, and I've found two slightly different expressions, which are as follows: $$H=\frac{1}{2m}(\vec{p}-q \vec{A})^2 ...
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Magnitude refers to number or number with units?

This question is about terminology for physical quantities. When we talk about magnitude (while talking about scalars and vectors) do we refer to just number or Number along with units? example: If ...
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Can you use PCR to make a standard kg?

While reading this question: Why do we still not have an exact definition for a kilogram? , I had a crazy thought. Using PCR, you make a known number of copies of a DNA strand where the length and ...