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Questions tagged [units]

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

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Unit of $eV^4$ for Density?

I'm going through this paper on electroweak burning, and I ran across the figure $100 GeV^4$ to describe energy density. I'd like an explanation as to how the units work out, and why this figure isn'...
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Thermodynamics: Units in calculations of heat (Q)

When calculating an unknown variable in the quantity of heat equation for a system, let's say mixing water of 80 degrees C and ice of -20 degrees C that achieves thermal equilibrium at 10 degrees C (...
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5answers
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Why are the units of angular acceleration the same as that of angular velocity squared?

According to this answer, the units for angular velocity squared are $\mathrm{rad}/s^2$. The units for angular acceleration are also $\mathrm{rad}/s^2$. Why is this the case?
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3answers
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What is the sound absorbing characteristic of a material called?

I understand that lead is one of the best acoustic barriers because it absorbs sound very well; in other words, it converts sound to heat. By comparison, other materials tend to either transmit the ...
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1answer
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Constants of proportionality in Force Equations/ Physics in General

I was in physics class and we were talking about the gravitational constant G (6.67 x 10^-11 Nm^2/Kg^2). The question came up: "Why does $F= (GMm)/r^2$ have a constant of proportionality and not $...
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Definition of a meter and Newtonian law of Gravity

Newtonian law of Gravity: $$F_g = \frac{m_1 m_2}{l^2} G$$ $$G = 6.7 * 10^{-11} \frac{m^3}{kg * s^2}$$ A meter is defined as: the length of the path traveled by light in a vacuum in $1/...
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Can a physical quantity be of different dimensions depending of the system of measurement?

When comparing the Wikipedia articles on the International System of Units, the Planck unit system, and the geometrized unit system one question arises: can a physical quantity be of different ...
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Write the dimension of 1D wave function? [closed]

I want to know how to find the dimension or unit of one-dimensional wave function
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35 views

Finding the unit of Pressure/Volume

Me and my friend are trying to find the exact unit of Power=Pressure/Volume. We know that the unit has to be W(J/s) so we try from the equation above: (Kgm²/s³)=(N/A)/V The right side will be: (Kgm/s²)...
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2answers
106 views

What are the units of probability density?

Units of probability density? If bound electron is thought of as a cloud of charge, and it's charge density is proportional to the probability density. Then coulombs /m3 proportional to?
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1answer
61 views

What is the mass of $N_A$ atoms of carbon-12?

With the recent redefinition of the kilogram, what is the mass of $N_A$ (Avogadro's constant) of carbon-12 atoms? $N_A$ was defined as exactly 6.02214076×$10^{23}$ atoms. Then how close would the ...
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How is a Kibble balance used in the new definition of the kilogram, and what's the connection between the balance and Planck's constant? [duplicate]

The BBC News article Kilogram gets a new definition says: How does the new system work? Electromagnets generate a force. Scrap-yards use them on cranes to lift and move large metal objects, ...
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1answer
45 views

What does the Planck-like charge $Q=\sqrt{\frac{\pi}{c\hbar \varepsilon_0}}$ represent?

While experimenting something with equations I got a equation of charge which is not Planck's charge, dimensionally it is correct. I used dimensions method to get this. $$Q=\sqrt{\frac{\pi}{c\hbar \...
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1answer
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Question on units for voltage equation of a voltage at a distance z from a single line charge

I have a very basic question on the units for the equation of the potential at a distance: $z$ from a single line charge. The electric potential due to a very long line charge at some distance $z$ is ...
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1answer
39 views

Unit vector in displacement

When we use vectors in physics why does the unit vector (for displacement) equals magnitude of 1 or magnitude of 1m?
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34 views

How physically are equal subdivisions on a meter scale made?

How are equal subdivisions on a meter scale actually made? For meter can be obtained easily by the duplication of the internationally accepted prototype of the meter but further how are equal ...
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2answers
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How to determine the units of my integral? [closed]

Given that I have some coefficient(i.e. a number) which is to be determined from a radial integral: $$b_{n00} = \frac{(2\pi)^{1/4}}{\sigma^{3/2}} \frac{1}{\sqrt{3}} [C(000|000)]^2 \int^{\infty}_{r = ...
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4answers
108 views

Why is the speed of light used to define the fourth axis of spacetime?

The four axes of spacetime are $x, y, z$ and $ct$, where $c$ is the speed of light, and $t$ is time. Why is the speed of light (not any other speed) used to define the fourth axis of spacetime? If ...
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1answer
45 views

How is the division of physical quantities into base quantities and derived quantities a matter of convention?

Several physics textbooks and even the SI-The International System of Units Brochure(8th-edition) says that, ''The division of quantities into base quantities and derived quantities is a matter of ...
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1answer
24 views

Coordinates in 1970 Labeyrie article

I'm reading the 1970 article by Labeyrie on speckles in astronomy and I encountered a small problem. The author uses two sets of coordinates, $(\alpha, \beta)$ and $(x, y)$, connected by Fourier ...
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0answers
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What is the unit of polarization mode dispersion?

I calculated the differential group delay (DGD) from measured data following a chapter in the book "Polarization Optics in Telecommunication" by Jay Damask. Basically, I measured a unitary matrix $U(...
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0answers
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What are the units for state vectors in QM? [duplicate]

Specifically, it seems that a state vector should be dimensionless because: $| \langle \psi | \psi \rangle |^2$ is a probability which is dimensionless However, I find myself doing manipulations ...
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1answer
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Meaning of units in the Heisenberg Uncertainty Principle

So we have the inequality $\Delta x\,\Delta p\geq \hbar/2$ Why is the uncertainty of position in meters? Isn't uncertainty measured in probabiliies? Does it make sense to say that the uncertainty in ...
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4answers
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Is a unit vector really unitless and dimensionless?

According to my textbooks, a unit vector has no units and no dimensions, but is only used to specify direction. It only shows the orientation of a corresponding vector in space. I think it's true, or ...
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0answers
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Electromagnetic four-potential plane waves expansion in SI units

In Mandl's book Quantum Field theory the expansion of the electromagnetic field is given by $$A^{\mu}(x)=\sum_{r,\vec{k}}\left(\frac{\hbar c^2}{2V\omega_{\vec{k}}}\right)^{1/2}\varepsilon^{\mu}_r(\vec{...
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Are the units of energy the same in higher dimensions?

In 3 spatial dimensions, $$[E] = [ML^2 T^{-2}]$$ Would it change in higher dimensions? If yes, then what would be the dimensions for 4 spatial dimensions?
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1answer
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Significant figures in multiplication with units

Why does it make sense to round to the smallest significant figure instead to the largest unit? If I have one measurement made to the nearest millimetre and another to the nearest picometre then why ...
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1answer
68 views

In the value of gas constant $R$, what kind of mole is it?

Wikipedia gives $$R=8.3144598(48)\, \rm J\,mol^{−1}\,K^{−1}$$ But I want to ask how is it possible to write $\mathrm{mol}$ without a suffix? I mean, we must determine if we have $1\ \mathrm{mol}$ of ...
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1answer
53 views

What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? [duplicate]

What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? For example, $1 \:\rm m/s$ mean that each second, we make one meter. Also, $1\:\rm m/s^2$ mean that each second the speed ...
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3answers
102 views

Expressing the conversion from units of time to units of space in special relativity rigorously

In their book Spacetime Physics, Taylor and Wheeler stress the analogy of the speed of light $c$ to a conversion factor $k$ which converts between miles and meters and subsequently convert freely ...
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1answer
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mathematically explain why add operators with different physical unit is wrong?

Suppose I have two operators $J^2$ and$J_z$ where they represent the length of angular momentum and its $z$ component respectively. Sure, it's legal to write new operators like $J^2-J_z^2$ or $J_x+...
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What does the unit “kcal/mol” mean?

I recently encountered units of energy written as $``\mathrm{kJ}/\mathrm{mol}"$ or $`` \mathrm{kcal} / \mathrm{mol} "$. I'm aware of the meanings of $`` \mathrm{kJ} "$ and $`` \mathrm{mol} " , $ ...
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2answers
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How do I add measurement units to a power-function relationship like $y = 0.17x^{0.52}$?

I have the equation $y = 0.17x^{0.52}$, where the units on $x$ are $\rm cm$ and the units on $y$ are seconds. I can't figure out how to put units on the constants so that they work out and I get the ...
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1answer
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I'm confused about electric flux?

In a previous physics class, I learned that the electric flux was $\vec{E}\cdot\vec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and ...
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1answer
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Intuition about the congruence of readings of Celsius and Fahrenheit scales at -40°C [closed]

At -40°C temperature, the Fahrenheit scale also shows -40°F. But how is this ever possible? They are two different scales! What's the intuition behind this?
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1answer
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Mass (as a unit) has no physical property [closed]

Einstein's GR or Newton's equation uses mass as unit or number. How can it cause gravity (physical phenomena)? For any physical phenomena to occur, there must be physical/chemical/biological/etc. ...
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Coincidental relation between ratio of masses, lengths and time intervals in the universe

The ratio between the largest and smallest lengths in the universe is about 10^41 and it's the same with time intervals. But for masses the ratio is about (10^41)^2. Is this purely a coincident or is ...
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1answer
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Can this quantity defined by exponentiating lengths be meaningful?

I just read Accurate predictions of coexistence in natural systems require the inclusion of facilitative interactions and environmental dependency in which they defined the following property:$^1$ $$\...
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1answer
86 views

Is there an MKS unit system in which electric and magnetic fields have the same measurement unit?

I'd like to know if there's an MKS unit system in which electric and magnetic fields have the same measurement unit. I couldn't find anything like that on the internet. Does that system exist? Do ...
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1answer
112 views

What is the value of absolute zero: $-273.15\ \rm °C$ or $-273.16\ \rm °C$?

What is the value of absolute zero? 0K= -273.15 °C Or -273.16 °C It has been confused in different scientific scriptures. The first definition on Dictionary.com, for example.
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190 views

Is it a coincidence that 1 liter water has a mass of 1 kg while 1 cubic meter has 1000 liters of water?

1 Cubic Meter has 1000 liters of liquid. Meter is a unit independent of Kilogram. Then why does 1 liter of water at max density (4°C) have a mass of 1 Kg?Is it a mere coincidence?
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0answers
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Geometrized units in Wald

I am trying to follow a derivation in this paper from Wald Specifically, at the end of the paper, just under Eq. 4.7 there is given the equation $$ Q/m \leq 2 B_0 m$$ where $Q$ is the system ...
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2answers
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Why are the dimensions of escape velocity correct?

How does this formula work, from a dimensional analysis perspective? $$ v_\text{escape} = \sqrt{\frac{2GM}{R}}$$ The way I'm thinking about it is that $G$ is in units $\text{N} \cdot \text{m}^2/\...
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2answers
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What does “as small as a fraction of an angstrom” mean?

I was reading my school textbook in which the following statement was given: The resolution of such an electron microscope is limited finally by the fact that electrons can also behave as waves! (...
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2answers
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How to put $c$ back into relativistic equations?

Many books set the speed of light $c=1$ for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though $G$ is still left as a constant): $$\begin{align} \mathrm{d}\tau^2 &...
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Stoney Units vs Planck Units

Why are the Stoney Units (excluding elementary charge) still shown to be different than the Planck Units when they can be divided by the square root of the fine structure constant which would make ...
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5answers
2k views

Does the magnitude of a physical quantity have units or is it just a plain number?

Does the magnitude of a physical quantity have units? For example, if a velocity vector is $36\ \mathrm{m\,s^{-1}}\ \hat{u}$, is its magnitude $36\ \mathrm{m\,s^{-1}}$ or just $36$? Also why?
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2answers
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Question about Radian as a unit

I'm having a hard time trying to understand the units between angular velocity and basic velocity of a circle. For angular velocity the units are Radian(s) per second(s) or degree(s) per second(s). ...
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1answer
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Pressure unit computation (feet of mercury, but applies also to foot of water..) [closed]

Grr this question makes me crazy. Here you can see that ftHg = 13595.1 kg/m3 × 1 ft × ɡ0 = ≈ 4.063666×104 Pa. (= 40636.664 Pa) https://en.wikipedia.org/wiki/Conversion_of_units (Pressure or ...
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Is the International System of Units complete?

Are there any known (measurable continuous) physical quantities, which are neither base quantities of SI, nor are derivable from the base quantities? In other words, are there any quantities which ...