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

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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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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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339 views

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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3answers
153 views

Is electronvolt a mass or an energy unit?

I always thought electronvolt was an unit of energy and I knew its definition, but in these days I got some doubts because I saw 2 times it was used as an unit of mass: in my school textbook, in an ...
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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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225 views

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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559 views

Why is the absolute zero -273.15ºC?

I can't find an answer of why the lowest temperature is -273.15ºC. Is it deduced theoretically or is it experimental? An explanation is that when any gas volume tends to zero, the temperature will be ...
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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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355 views

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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131 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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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
118 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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2k views

What is the Units for Thermal conductivity?

What are the units for thermal conductivity and why?
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1answer
125 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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1answer
71 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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1answer
190 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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1answer
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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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1answer
219 views

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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0answers
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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
248 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 ...
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1answer
164 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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Understanding units manipulation (speed of falling coconut after 20m)

When I was on holidays, I was told a story about how someone passing under a palmtree and almost got a coconut fall on his head. Given that these palmtrees where about $20m$ high, we wondered at what ...
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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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Is electron volt an alternate unit for electric potential? [closed]

My question is: Can an electron volt be considered an alternate unit for electric potential?
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1answer
58 views

Is there a name for a quantity that represents (volumetric) flow per unit of mass?

In a lot of medical literature about blood flow in the brain, researchers denote the amount of volumetric blood flow that passes through a certain amount of brain tissue as "cerebral blood flow". ...
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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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To what extent are quantities fundamental?

Arguably the most well-known and used system of units is the SI-system. It assigns seven units to seven ‘fundamental’ quantities (or dimensions). However, there are other possible options, such as ...
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1answer
165 views

What is volume * mass be called? [closed]

I need a denotation for a rather unusual unit. $$ \frac{m}{V} $$ is called density. So what is $$ m \cdot V $$ called? Is there a denotation for it? I'd like to get a denotation that could somehow ...
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1answer
771 views

How can Young's modulus be dimensionless, but still have units? [closed]

According to this wikipedia entry: Young's modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore, Young's modulus has units of pressure. From ...
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156 views

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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387 views

Formulas for kinetic energy

I was reading ABC of relativity from Bertrand Russell and some formulas about kinetic energy caused me some problems. Here is the extract : The kinetic energy is, in the usual form ...
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244 views

In what order should unit symbols appear?

I am trying to represent the result of a dimensional analysis calculation and I can't find an official document that lists the order that unit symbols should appear. For example, when I google ...
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1answer
61 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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115 views

Help me check units [closed]

I need to check units in this equation, I know, that there's Pa in the numerator, but what about the denominator? $p_1$ - pressure in [Pa] $T_1$, $T_2$ - temperature in [K] $\rho_w$ - density $g$ - ...
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101 views

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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309 views

Physical representation of volume to surface area

I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume ...
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1answer
344 views

Convert units from cal cm^-1 day^-1. to Wm-2

I am trying to calculate the energy budget of a water body and the last term I'm trying to calculate is the energy advected from the water body ($Q_v$). This equation is given by: $Q_v = V ( (T_1 - ...
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1answer
120 views

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 ...
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1answer
262 views

What are units actually?

This question is about the concept of units in physics. Firstly - do units have a formal mathematical definition? How are they different from pure numbers? Are pure numbers defined to be ratios of ...
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109 views

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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2answers
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Why metric system uses kilogram as a basic SI unit?

SI system uses all (that I know) measurement basic units as 1 (single) instance: meter, second, ampere, etc, except the KILOgram. It already defined with 1000 multiplier (kilo). It prevents from ...
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1answer
859 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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1answer
117 views

Magnetic Field and the Speed of Light

Is it just a historical choice that both magnetic field and the Lorentz force equation include the speed of light? I figure that whoever wrote up the equations (in cgs!) could have put both factors ...
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1answer
154 views

CGS Units for Magnetism

Why does the formula for magnetic field force include the speed of light in the denominator in cgs units? Where does the extra $c$ go in SI units?
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Does the unit of a quantity change if you take square root of it?

For example, I have a mass, m = 0.1kg and I square root it, giving me m = 0.316 (3s.f.) does the unit still stay as kg, or does it change?
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What Physical Quantity has SI Unit $kg \cdot m$,? [duplicate]

What is the physical quantity that has SI (System International) unit of $kg \cdot m$ (kilogram meters)?
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141 views

Units for physical constants

Someone told me that units for $G$ and $\epsilon_0$ (gravitational constant and Coulomb's constant) are placed there simply to make equations work dimensionally and that there is no real physical ...