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

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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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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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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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319 views

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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869 views

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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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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509 views

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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190 views

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 ...
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Can x and y axis have different scales? [closed]

In a graph on reflection, can i give the x axis a scale of 4 cms = 10 degrees , and the y-axis a scale of 2 cms = 10 degrees? Will it affect the readings?
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251 views

Finding the correct units for the energy-momentum tensor?

I'm trying to understand the energy-momentum tensor $T^{\mu\nu}$ but I'm confused about the units. My textbook says the components of $T^{\mu\nu}$ are $\mathrm{Jm^{-3}}$. Four-momentum is is given ...
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121 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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146 views

Non-Dimentionalization of equations

I am trying to understand a paper in which they mention; " We non-dimentionalize the problem hereafter by selecting mass, length and time units such that the fluid density $\rho\equiv1$ the ...
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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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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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297 views

What is the Units for Thermal conductivity?

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

What units are needed for the variables when I want the result to be in $erg$ [closed]

$erg$ is an Energy unit, which means that it is equal to $\frac{mass{\cdot}distance^2}{time^2}$. If I want to calculate the kinetic energy of a body in erg units, in what units should the distance and ...
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138 views

Clarification on factors of $c$ in the Lorentz' force

I was told that Lorentz' force is given by $${\bf F}= q{\bf v} \times {\bf B}.$$ But I have read that it is given by $${\bf F}= \frac{q}{c}{\bf v} \times {\bf B}.$$ Why have these two relations ...
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215 views

Conversion from barn unit to square meter?

I read Wiki: http://en.wikipedia.org/wiki/Barn_(unit) on this and calculations under the 'Conversion from squared prefixed SI units' do not look like correct. Is 1fm^2 = 10 mb ? (or 1b = 100m^2 ) ...
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Can I calculate the maximum concentration of sucrose that will dissolve in water at STP using physical constants?

I am interested in identifying the maximum solubility of sucrose in water. Can this value be estimated based on the physical properties of sucrose? Eventually I will need this in degrees Brix (%w/w). ...
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520 views

Converting Notes to Milliseconds

Given a note duration (whole, half, quarter, etc.), a tempo (in beats per minute), and a time signature, how long does that note last in milliseconds?
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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: ...
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83 views

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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127 views

Unit analysis of a Fourier transform

This is an extension of a Phys.SE question I asked earlier, Fourier transform of two pulses of light. I start with 2 Gaussians, represented by the equation $e^{-(t/a)^2}\times e^{2\pi i d ...
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525 views

When should angles be expressed in degrees vs. radians?

I am trying to calculate the albedo of a given latitude by following the methods of Brutsaert (1982), I have copied the formula below: 3.6 Shortwave and long-wave radiative fluxes Albedo ...
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112 views

Conversion of the units BeV (US) and GeV (UN)

What is the difference in the definition of a billion electron volts in United states (US) and United Nations (UN)? When the US people say billion, do they mean $10^{12}$ or $10^9$?
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143 views

Working with atomic (?) units in solid state physics

I'm having some troubles understanding the units used in solid state physics paper. In the paper I read $\Lambda a \sim 1$ where $\Lambda$ is a momentum cutoff and $a$ is the lattice spacing of a ...
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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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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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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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103 views

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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209 views

What is electron density and its unit in plasma physics?

I can not find (through Google search engine) that what means electron density and what is its unit? and what is there relation between electron density and electrical conductivity?
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Special relativity, spacetime, velocity and units

We all know that space and time are the fundamental units, means no mathematical expression can express their relation to other variable fundamentally. But as we know that moving rod has a contracted ...
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915 views

What is the physical interpretation of force times area?

I know that $\text{Force} \times \text{Distance = Work}$. But, what would be the physical meaning of $\text Force \times \text Area?$ Is such a quantity used in physics?
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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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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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Units describing the behavior of neutrinos

http://proj-cngs.web.cern.ch/proj-cngs/Download/CNGSDGVE/cngsdgve.pdf on page 13 I read that "the present plan is to provide nu_mu neutrinos with an energy between 5 and 30 GeV." Wikipedia neutrino ...
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Is $kg_f$ the same everywhere in the universe?

A textbook question says that a vehicle weighs $25kg_f$ on Earth, and asks us to consider certain issues related to its behaviour on the moon. My question is, does the unit kilogram-force $kg_f$ ...
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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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309 views

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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Dividing values with units

I'm reading about the subject of heat in a basic physics book. If I am not mistaken the formula to work out how much energy is required to increase the temperature of water is ...
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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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898 views

Units of Distance, Pressure, and Temperature [closed]

I need to store data. I'd like to store them in Metric units and use a tool to convert them to and from other units that these data points will be displayed in. As the title states, my constraints ...
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units of measure

This question is rather historical one. kilometres can be defined in metres, metres in centimetres, centimetres in millimetres. There must be some elementary unit (like millimetre or smth.) which ...
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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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Would a truly physical oscillation still be measured in hertz?

I recently bought a new scroll saw and was commenting to someone about how it was a relatively slow saw... low ... RPMs (thinking like a circular saw). Then it occurred to me that not being a circle, ...
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The units of gain and number of atoms in population inversion in a laser

I am following my university course notes on amplification in laser media, and have come across expressions for the gain of a medium, but the notes are not exactly rigorous... The expression given for ...