Questions tagged [units]

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

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How can the magnetic $B$-field of a photon or light wave be directly compared to the electric $E$-field if the units are different? (Tesla vs. V/m)

I know that the electric field of an electromagnetic wave has the strength (or intensity?) of the magnetic field times the speed if light $c$. (E = B × c)... But, the units are not quite the same (I ...
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How to conceptualize the unit Temperature?

For a long time, I was under the impression that Temperature is just a shorthand for the "average energy" within a system, but I discovered this is wrong (although sometimes this is a valid ...
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1 answer
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I am stuck on Precision Applying Problem [closed]

The stability of the Cesium Clock used as an atomic time standard is such that two Cesium clocks would gain or lose $1$ s with respect to each other in about $300,000$ y. If this same precision were ...
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What is the relationship between magnetic field quantities $B$ and $H$ in cgs units?

In cgs units permeability of free space is dimensionless. If so, then in cgs units won't $B$ and $H$ have same units as they are related by equation: $B=\mu_o H$ But instead why they have different ...
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What is the difference whether a space is used between number and unit for temperature? [closed]

When talking about temperature, or temperature change, -32.5 ℃ (with space), and -32.5℃ (no space) are two common expressions. Are they the same? If there is no space is used, there is a problem about ...
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Name for inverse of heating or cooling rate?

I would call the average change in temperature of a body per unit time « cooling rate » or « heating rate » depending on the sign. Is there a name for the inverse of this quantity, ie the time it ...
15 votes
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Is the equal sign in "$0 ^\circ \mathrm{C} = 273.15\, \mathrm{K}$" fair?

I'm in doubt whether the equal sign in an expression like "$0 ^\circ \mathrm{C} = 273.15 \,\mathrm{K}$" is fair because, normally, if $A=B$, then, say, $2A=2B$, which is hardly applicable to ...
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Pankove optical absorption equations: cgs problem?

I'm embarrassed to be asking this question here, but I've been beating my head against an equation for two weeks and can't get the numbers to work. I'm trying to plug in numbers into Jacque Pankove's &...
1 vote
3 answers
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Why gravitational constant $G$ does not have the factor of $4π$?

We know that electrostatic constant $K=\frac{1}{4\pi\epsilon}$. This $4\pi$ came from the surface area of the surface in which charge is enclosed. Then, why don't gravitational constant has the factor ...
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Unit analysis of classical equations, and why charge and mass may be manifestations of the same thing? [closed]

Consider Newtons force for universal gravitation, $$F_g=G\frac{m_1 m_2}{r^2}.$$ Nothing new here, but bare with me. This is a strange idea, hard to articulate adequately without a greater ...
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What determines the existence of a physical dimension, as in dimensional analysis?

Dimensional analysis in physics is based on the idea that only commensurable quantities can be added, subtracted, equated or otherwise compared. The five dimensions which appear in dimensional ...
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Computing the maximum force a rod can bear [closed]

Suppose I had a rod of diameter $d$ composed of some material with tensile strength $T$. If I then exterted a pulling force $F$ on the ends of the bar, how do I compute the force $F$ for which the ...
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1 answer
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Kinetic energy and de Broglie wavelength of an electron [closed]

The question in the problem sheet reads The de Broglie wavelength of a non-relativistic (nr) electron with kinetic energy E$_{kin}$ can be written as $ \lambda_{nr} = \frac{\delta}{\sqrt{E_{kin}}} \;\...
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Calling angles dimensionless and simultaneously distinguishing between numbers and angles is inconsistent, isn't it?

The SI Brochure says that each angle is the ratio of two lengths - i.e. a number - and therefore a derived and dimensionless quantity. On the other hand, the papers [1] and [2] suggest that angles are ...
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Solving an ODE numerically with different units

I am simulating a leaky integrator with $R_m = 10^8 \, \mathrm{\Omega}$ and $C_m = 10^{-10} \, \mathrm{F}$ with an input current of $I_{in} = 10^{-9} \, \mathrm{A}$ for $0.1 \, \mathrm{s}$: $$C_m \...
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Fundamental Units and Concentration

I am working with the Cahn-Hilliard equation which is typically given in terms of a dimensionless concentration, $u$. I generally find myself being confused when dealing with dimensional equations ...
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Free energy Functional and its Relation to Pressure and Chemical Potential

I am reading a paper and trying to follow along some of the mathematical steps and reasoning; however, I can't quite understand one aspect. The authors give an expression for the free energy ...
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3 answers
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Unitless variable screws up calculation

All, the following equation represents the budget of the specific humidity $q$ (which is the ratio of mass of the water vapor to the mass of the dry air, usually written as gram/kg or kg/kg). $$ \...
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Does taking the $\log$ of a quantity change the unit of the quantity?

\begin{align} &= c [P - b \ln(P+b)]_1^{500} \\ &= 0.125 \frac{\text{cm}^3}{\text{g}} \times \left[\begin{aligned}&500 \text{ bar} - 2700 \text{ bar} \times \ln(500 \text{ bar} + 2700 \text{...
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The utility of HorsePower vs Torque [closed]

All vehicles have only 1 gear Final-drives allow peak RPM (HP) at red line = 35 MPH Wheel-sizes are equal Tires have perfect traction (yet, no rolling resistance, etc) Goal: isolate all variables ...
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Why angle and solid angle not included in fundamental physical quantity? [closed]

So I recently studied about physical quantities. I doubt what actually Fundamental physical quantities is?? Book simply says it as 'quanties which doesn't depend on other physical quantities" ...
14 votes
3 answers
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Isn’t natural units prone to mistakes?

Suppose I am deriving a length contraction formula using natural units. If I arrive at $L = L_0 \sqrt{1 - v^2}$, I know that I should divide $v^2$ by $c^2$ to get the correct answer in SI units. But ...
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Can you measure the space-time interval using a meter? [closed]

The unit of the space-time interval is the meter: $$ (\mathrm{d}s)^2 = (c \mathrm{d}t)^2-(\mathrm{d}x)^2-(\mathrm{d}y)^2-(\mathrm{d}z)^2. $$ Can it be measured with a meter? How?
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Are there Imperial or United States Customary units of electromagnetism, luminous intensity, or moles?

In the UK, Boris Johnson's somewhat beleaguered government has recently announced a consultation on using Brexit to ensure that "more choice can be given to businesses and consumers over the ...
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Gyromagnetic ratio: units problem

I tried to calculate the gyromagnetic ratio of the proton with this formula: $$g_p = \frac{2.m_p.c^2}{e.\hbar.c^2}.\Delta E \approx 5,28$$ with $m_pc^2 \approx 938 \ \mathrm{MeV}$, $e \approx 1,67.10^{...
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2 votes
1 answer
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How do I determine what physical constants can be combined to derive a set of natural units?

I am looking into natural units (units of measurement based only on universal physical constants). Different systems of natural units use different physical constants as their defining constants. If I ...
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Couldn't understand an example used in explaining fundamental and derived quantities

In my book under topic of fundamental and derived quantities, there is an example which is supposed to explain this concept and it goes like this, As a simple example, if a unit of length is defined, ...
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Magnetic flux from maximum induced emf as a function of angular velocity?

I've done an experiment where I have a small rotating coil in a uniform magnetic field and I've measured the induced emf in the rotating coil as a function of time for several different angular ...
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Different units of measure for the specific intensity and the components of the Stokes vector

Good morning to all, I'm a bit confused about the fundamental physical quantities adopted in the theory of radiative transfer. In particular, many texts show the scalar integro-differential equation ...
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4 answers
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Why is $(\text{kg} \cdot \text{m}^2)/\text{s}$ written as "Joule second" when there is no joule present, and time is divided and not multiplied?

The Joule is $(\text{kg} \cdot \text{m}^2)/\text{s}^2$, which is not contained in $(\text{kg} \cdot \text{m}^2)/\text{s}$, the Joule second. So, why does the unit name contain "Joule"? Also, ...
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CGS of resistance

What's the CGS unit of resistance? Is it the same as that in SI system, i.e. ohm (Ω)? I googled but found no explicit answer.
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Unit issues with commutator relations with two dependent variables

Suppose I have the following commutator relation for an operator $a[x,\omega]$ which depends on position $x$ and frequency $\omega$ $$ \left[a[x,\omega],a^{\dagger}[x^{\prime},\omega^{\prime}]\right]=\...
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Notation for rule of thumb, without breaking dimensional homogeneity?

I'd like to know how to write rules of thumb in a concise way, without breaking dimensional homogeneity. For example, if a runner has an average speed of ~10 km / h, an approximation of the covered ...
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1 answer
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When scaling down a universe, what is scaled down, and how to calculate gravity?

Assume I want to scale down Earth so that it fit into a 500x500 units (pixels) cartesian plane, at a scale of 1:1,000,000. Earth, with a radius of 6,371,000 meters, now has a radius of 6.371 units. ...
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What is unit system in this reduction process?

I have read "The Stopping and Range of Ions in Solids", which is published in 1985 about ion implantation. There is a equation in P.53 : $$ \varepsilon=\frac{32.53M_2E_0}{Z_1Z_2(M_1+M_2)(Z_1^...
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Why are there two different units for charge; the coulomb and elementary charge? [closed]

Why are their two different units for $q$ charges?
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Units of damping terms for harmonic oscillator

I understand that in the equation of motion of a simple harmonic oscillator $\ddot{x} + \omega_0^2 x = 0$, $\omega_0$ has dimension inverse time. Since solutions are of the form $x(t) = A \cos (\...
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Why electrical current is base quantity instead of electrical charge? [duplicate]

I thought base quantities are defined as independent quantity. But I realized Electrical Current which usually notated as I for ...
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Transduction coefficient of an electromechanical system

I have been recently doing a physics experiment which requires me to determine the transduction coefficient of a speaker system, undergoing electromechanical resonance, in an AC circuit. The quantity ...
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1 answer
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Why are people using 'lightyear' as a measurement of time? [closed]

I came across 2 people in an open forum, who are college students, who that agree using the term 'lightyear' as a measurement of time is correct. Their context was "This country's technology is ...
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Unit of a log normal probability density function

How do I find the unit of a log-normal probability density function?
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Ratio of thermal energy in a parcel of water between two time periods (metric vs imperial units)

I am having a problem figuring out something that should be quite basic with determining the ratio of the thermal energy content of a parcel of water (let's say $1 kg$) in between two time periods and ...
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On "cosmic flux" units

I've trouble understanding the following graph, taken from Wikipedia: It's supposed to show the cosmic ray flux vs particle energy. I've never seen a "flux" written in these units... Why ${...
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Second functional derivative and its units

Say I have a functional $I[\phi,g]$ with $\phi(p)$ and $g(p)$ functions from $\mathbb{R} \to \mathbb{R}$. Also say that this functional obeys the property: $$\frac{\delta I}{\delta g(p)} = -(g(p))^{-1}...
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Do squared units grow in size or shrink in size if the value can be represented by a different unit?

I was doing a very simple equation, $\frac{1}{2}kx^{2}$, when I realized that, if I represented the distance in centimeters, $x^2$ would grow in size (because x is 10 centimeters), but if I ...
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Conversion factors derivation

Unit conversion chart Queries regarding MKS to CGS system for the following formulas : Force $=$ Newton (MKS), Dynes (CGS) $$\mathrm {1\ N = 10^5 \ dynes}$$ Work $=$ Joule (MKS), Ergs (CGS) $$\...
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Imperial units - mass and force

I was rudely informed on an answer here that 1 lb is a force and I 'didn't understand' mass. (I am not interested in relative merits of systems of units - only dimensions..) Now - we know that Force ...
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Units in vector spaces

I am confusing myself about where physical quantities become mathematical objects. Where does one end and the other begin? E.g. displacement $\vec{s}$. A displacement is a physical quantity that can ...
2 votes
2 answers
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Electromagnetism using differential forms, question about names and units

When formulating classical electromagnetism using differential forms, Maxwell's equations can be written as $$ \begin{align} dD &= \rho \\ dB &= 0 \\ dE &= -\dot{B} \\ dH &...
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Calculating photographic exposure - confused about luminance, illuminance, luminosity etc

On first glance this sounds like a photography SE question, but it's more concerned with physical measurement of luminosity, luminance etc - the photographic application of the value calculated is ...
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