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Questions tagged [units]

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

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435 views

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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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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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
131 views

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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1answer
314 views

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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1answer
42 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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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
81 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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63 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
116 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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2answers
103 views

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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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
248 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
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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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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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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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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
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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
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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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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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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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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
92 views

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
387 views

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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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
157 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
149 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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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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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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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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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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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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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 ...
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Why are “degrees” and “bytes” not considered base units

From Wikipedia: The SI base units and their physical quantities are the metre for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for ...
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1answer
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Does it make sense to multiply a unit by a negative number?

I was thinking about the way our system of units of work, and I realized that we have been multiplying units (such as for lengths) by negative numbers, when dealing with vector quantities; positive ...
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3answers
503 views

Magnetic $H$ field unit in cgs system

I'm studying an old E&M textbook which uses cgs unit system. I'm re-writing the formulas in SI unit. The book says $\vec{H}=\vec{B}-4\pi\vec{M}$. So I guessed that $H$ should have same unit as $...
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Downsampling the wavelength spacing of spectral radiance

I have spectral radiance measurements, $L_e$, that I need to downsample, and I want to make sure I do this correctly. Let's say the measurements are a constant value of $5\times 10^{-3}\: \rm W \: m^{-...
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1answer
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Units caculation in the article don't match for reynolds numbers higher than 1

The article discusses the forces acting on a falling object in respect to the drag forces and reynolds numbers. The article suggests for varying Reynolds numbers, the force of drag equation is written ...
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4answers
698 views

Why does this paper use 1/cm for units of frequency?

Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency. Here is an excerpt: It doesn't seem like wave number, as they clearly call it frequency. What's going on here? $^*$ ...
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2answers
187 views

Infinite plane gravity: what is “mass density per unit area”?

Recently I learned that the gravity of an infinity plane is independent of the distance from that plane. In fact it is $$g = 2\pi G \sigma$$ where $\sigma$ is "the mass density of the plane per unit ...