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

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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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52 views

Confusion about units of angular momentum

According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec I am confused about the derivation for this. Here is what I have done: $$L = I \cdot \omega \\ = m \cdot r^2 ...
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2answers
95 views

Why do we set $x^0 = ct$ instead of $x^0 = t$?

When we deal with Special Relativity and we start considering spacetime instead of space and time each at once, we usually see books saying that we consider a space with four coordinate $x^\alpha$ ...
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Maxwell's Equations: Induction

What is the reason for some writing Faraday's Induction Law as $$ \nabla \times E= -\frac{1}{c}\frac{\partial B}{\partial t} $$ versus $$ \nabla \times E= -\frac{\partial B}{\partial t} ?$$
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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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57 views

What volume of helium at standard ambient pressure and temperature is required to lift one kilogram of mass? [closed]

I used the Ideal Gas Law PV = nRT where P is the pressure of the gas P = 1.033 kgf/cm squared V is the unknown volume of the gas n is the amount of substance of ...
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Units in time dilation calculation

I am currently working through Brian Greene's "World Science U" course on special relativity, and I have a question regarding one of the calculations performed for an exercise on time dilation (MODULE ...
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38 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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33 views

Convert constant of gravitation to days and AUs

I'm working on a problem with celestial bodies and for my purpose days and AUs are more appropriate units than seconds and meters. So I tried to convert the constant of gravitation, $G$, like this: ...
3
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55 views

How can Planck units be consistent with conflicting dimensions of mass?

I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = ...
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63 views

What is dimensional units/quantity and dimensional state

First, I am not a native English-speaking student so I am not good at physics definitions in English. I participated in the MIT e-learning course on classical physics. The 1st lesson is about 3 ...
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149 views

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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37 views

The exact definition of conjugate momentum density

After checking various websites, I've seen the conjugate momentum density defined as either: \begin{align*} P_r ~=~ \frac{\partial \mathcal{L}}{\partial \dot{A}_r} \end{align*} or \begin{align*} P_r ...
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65 views

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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Does physics have some division schema which divide physical amounts into these two classes?

Does physics have some division schema which divide amounts into these two classes? : A) amounts which can be counted by natural numbers (for example many units can be counted by number of ...
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What's the dimensionality of a solid angle?

I haven't seen this explained clearly anywhere. Solid angles are described usually as a fraction of the surface area of a unit sphere, similar to how angles are the fraction of the circumference of a ...
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What is the constant appearing in the low energy action?

Usually one finds this expression for the low energy action $$S = \frac{1}{2\kappa_0^2}\int d^D X\; \sqrt{-G}\; \mathrm{e}^{-2\Phi}\,(R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4 ...
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54 views

Dimensional analysis and the interpretation of measures [closed]

-- motivation for the question In the process of taking measures, selected amounts are chosen to be the reference (kg,m,s,..) and a measure is a comparison between 2 quantities, a ratio. When a ...
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Why do these equations result an incorrect unit for acceleration?

Hello everyone. Imagine an object moving around a certain point on a circular orbit. Magnitude of the velocity is constant during the motion ($|v|$). The orbit radius is $r$. (I'd better notice ...
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564 views

Why does Coulomb's constant have units?

I think of Coulomb's constant as a conversion factor (not sure if this is correct). Kind of like how you would do calculations in kg and then times it by the conversion constant to convert your answer ...
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79 views

How is a standard unit divided into equally smaller or fractional units physically/experimentally?

Consider the standard unit of length: meter. How was it divided into decimeter, centimeter, millimeter, etc. when there were no shorter lengths than the standard ? What is the physical/experimental ...
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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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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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74 views

Units of the PDF in the Lattice Boltzmann Method

In the Lattice Boltzmann method we require (based on mass conservation) that the sum of the distribution functions for a node is equal to the density, i.e. $$ \sum_i f_i = \rho $$ But what units do ...
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Is negative 20 psi / 1.5 bar possible?

If I understand correctly, negative pressure usually means relative pressure: the difference between inside and outside. If outside is normal (1 bar, 15 psi, 100 kPa etc), how low can the (relative) ...
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183 views

Integrating equations with units

I was looking through an old copy of Barron's AP Physics and found this problem relating to impulse which I was initially confused about how to integrate. Example 6.1 During a collision with a ...
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Stokes-Einstein's formula results in incorrect units for rotational drag coefficient

The Stokes-Einstein-Sutherland relationship, $$D = \frac{kT}{ 6 \pi \eta a}$$ where $D$ is the translational diffusivity is well known. A similar relationship is used to calculate the rotational ...
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160 views

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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Reliability of time dependent measurements

How is a "baseline" established. When an experiment is performed to verify the reliability of something like carbon dating. How do we know the results we get over the period of the test is still ...
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571 views

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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669 views

Why is the change of temperature $\Delta T$ measured in Kelvins, degrees Celsius, etc.?

Let me start by apologizing if this question seems pedantic and say that I'm not very familiar with physics in general, as I'm a math major instead. Anyway, say a body changes from temperature $T_1$ ...
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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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What is the opposite of the Planck length?

What "large size" unit of length could be considered at the opposite end of spectrum from Planck's length? Is there a table of smallest and largest value for various physical quantities that can be ...
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Units INSIDE of a Dirac Delta function

I know that the units of a Dirac Delta function are inverse of it's argument, for example the units of $\delta(x)$ if $x$ is measured in meters is $\frac{1}{meters}$. But, my question is what are ...
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Age of the universe in years

It seems to be commonly accepted that the Big Bang occurred roughly 13.7 billion years ago. My question is what is the meaning of the year in this context? When I type year definition into google, ...
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Basic Physics Question [closed]

I'm having a difficult time answering this question. I think I'm just converting the units wrong somewhere: You're the CEO of a courier company, and you decide to select an electric car for your ...
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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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Is the number 1 a unit?

In dimensionless analysis, coefficients of quantities which have the same unit for numerator and denominator are said to be dimensionless. I feel the word dimensionless is actually wrong and should be ...
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Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is ...
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How does (kg/m^3) * (m/s^2) * (m) come out to be units of N/m^2? [closed]

To me it seems to come out to be kg/(m*s^2). Is this somehow equivalent to N/m^2?
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2answers
107 views

How do we deal with irrationals in Physics? [duplicate]

This question is really very basic: how do we deal with irrationals in Physics? If for instance, in some meaningful calculation we get a length of $\pi$ meters, or a force of $\pi$ Newtons, how should ...
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297 views

What is the Units for Thermal conductivity?

What are the units for thermal conductivity and why?
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124 views

Where is the missing gram unit in this expression for energy loss?

In the discussion of "Landau Straggling", the following expression comes up for the energy loss $\xi$ in Landau's original paper: $$\xi = x\frac{2\pi N e^4\varrho\sum Z}{mv^2\sum A}$$ Here $N$ is ...
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60 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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119 views

About units and plural form

The plural form of physical units are always confusing me. I asked some senior students, some of them said we need to use plural form of units but some said units are always singular. For example, 1 ...
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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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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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Why was the conversion factor of the metric unit bar chosen the way it was?

The unit bar for pressure is clearly a metric unit, but its order of magnitude is a bit strange. In the centimeter–gram–second system of units we have: ...
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What is the meaning of $G/cm^2$?

I'll prefix this question by stating that I am not a physicist, I am a programmer. I am working on updating a (very old) program that calculates the performance of a magnet. This whole program is in ...
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1answer
175 views

Functional derivative and units

The both sides of below equation don't give the same units, e.g. $$ \frac{\delta}{\delta \phi (\tau)}\int_a^b \phi (\tau') d\tau'=1\;. $$ where $a<\tau<b$. To show this assume that the field ...