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

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What is a proportionality constant? (Planck's constant)

I understand that Planck's constant is essentially the ratio between the energy of a photon and its frequency. There are 2 things that im trying to verify: isn't the number that Planck's constant ...
3
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2answers
203 views

Exponential or logarithm of a dimensionful quantity?

I have a unit measure, say, seconds, $s$. Furthermore let's say I have a dimensionful quantity $r$ that is measure in seconds, $s$. What is the unit measure of $e^r$? ($1/r$ is in $Hz$.) My question ...
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81 views

double of temperature

I'm not a physicist, but I was having a discussion with a friend and I could not convince her about the main point. I asked her: "If I am in a place which temperature is 10ºC and she is in a place ...
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1answer
40 views

Does the unit of Inertia include radians? [duplicate]

The unit for angular acceleration $\alpha$ is: $$\mathrm{rad/s^2}$$ The unit for torque is $\mathrm{Nm}$: $$\mathrm{kg\ m^2/s^2}$$ And their relationship with Inertia is: $$I = \tau/\alpha$$ So ...
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1answer
71 views

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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2answers
119 views

Why do we set $x^0 = ct$ instead of $x^0 = t$?

When we deal with Special Relativity and we start considering spacetime instead of space and time each at once, we usually see books saying that we consider a space with four coordinate $x^\alpha$ ...
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2answers
69 views

Maxwell's Equations: Induction

What is the reason for some writing Faraday's Induction Law as $$ \nabla \times E= -\frac{1}{c}\frac{\partial B}{\partial t} $$ versus $$ \nabla \times E= -\frac{\partial B}{\partial t} ?$$
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1answer
88 views

Why are cgs units the norm in astrophysics?

Other physics communities, e.g. the particle physics one, have their own set of units, custom-tailored to their own needs. Now, the astrophysics community is somewhat similar, in that a lot of ...
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1answer
85 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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2answers
100 views

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 ...
2
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1answer
59 views

Is there a standard reference where entropy is set equal to zero in property tables?

For practical considerations, it seems that entropy is only meaningful as a difference between states, like $\Delta s$ going from state A to state B. For an ideal gas, for instance, standard formulas ...
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1answer
45 views

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: ...
3
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1answer
68 views

How can Planck units be consistent with conflicting dimensions of mass?

I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = ...
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2answers
101 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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3answers
164 views

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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1answer
51 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 ...
2
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2answers
133 views

Units of the Stokes-Einstein rotational diffusion coefficient

The Stokes-Einstein rotational diffusion relation tells us that we can write down a rotational diffusion coefficient for a sphere as: $$D_r \approx \frac{k_B T}{\zeta_f} \approx \frac{k_B T}{(8 \pi ...
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2answers
86 views

Does physics have some division schema which divide physical amounts into these two classes?

Does physics have some division schema which divide amounts into these two classes? : A) amounts which can be counted by natural numbers (for example many units can be counted by number of ...
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415 views

What's the dimensionality of a solid angle?

I haven't seen this explained clearly anywhere. Solid angles are described usually as a fraction of the surface area of a unit sphere, similar to how angles are the fraction of the circumference of a ...
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0answers
33 views

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 ...
0
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1answer
111 views

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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8answers
802 views

Why does Coulomb's constant have units?

I think of Coulomb's constant as a conversion factor (not sure if this is correct). Kind of like how you would do calculations in kg and then times it by the conversion constant to convert your answer ...
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1answer
92 views

How is a standard unit divided into equally smaller or fractional units physically/experimentally?

Consider the standard unit of length: meter. How was it divided into decimeter, centimeter, millimeter, etc. when there were no shorter lengths than the standard? What is the physical/experimental ...
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2answers
105 views

When “weight” of an object is listed, is it really the mass or the weight?

I Have read an earlier post regarding this, but the answer wasn't perfect enough or I didn't understand so! Let me put it to clear, I know difference between weight and mass. Also I know the ...
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3answers
171 views

What does the decay constant mean?

In my curriculum, the decay constant is "the probability of decay per unit time" To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a ...
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1answer
119 views

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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834 views

Is negative 20 psi / 1.5 bar possible?

If I understand correctly, negative pressure usually means relative pressure: the difference between inside and outside. If outside is normal (1 bar, 15 psi, 100 kPa etc), how low can the (relative) ...
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2answers
360 views

Integrating equations with units

I was looking through an old copy of Barron's AP Physics and found this problem relating to impulse which I was initially confused about how to integrate. Example 6.1 During a collision with a ...
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1answer
107 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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2answers
272 views

Why can't the units of work and torque be interchanged? [duplicate]

When I'm studying about work and torque, I found that their unit are the same. But, why don't we use Joule (unit of work) instead of Newton-meter (unit of torque)? Since $\mathrm{1\ Joule = 1\ Nm}$, ...
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25 views

Reliability of time dependent measurements

How is a "baseline" established. When an experiment is performed to verify the reliability of something like carbon dating. How do we know the results we get over the period of the test is still ...
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778 views

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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1answer
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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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1answer
300 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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3answers
242 views

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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145 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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3answers
197 views

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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213 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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357 views

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 ...
4
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3answers
459 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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2answers
1k views

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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5answers
346 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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125 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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1answer
609 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?
2
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2answers
114 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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3answers
1k 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
67 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
168 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
126 views

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. ...