Tagged Questions

Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

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16
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5answers
2k views

How can the speed of light be a dimensionless constant?

This is a quote from the book A first course in general relativity by Schutz: What we shall now do is adopt a new unit for time, the meter. One meter of time is the time it takes light to travel ...
4
votes
2answers
165 views

Where might hertz per dioptre actually be useful?

I once came across the strange, artificial unit "hertz per dioptre", which is dimensionally equivalent to "metres per second". Could this unit, by some stretch of the imagination, be used in some ...
3
votes
0answers
145 views

Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
2
votes
2answers
3k views

converting power spectrum to photon flux density

So I'm having trouble converting units and was hoping somebody could point out where I've gone wrong... It seems I'm missing something fundamental. a Power Spectrum has units $kW/m^2-\mu m$ for the ...
0
votes
3answers
395 views

What physical quantity has SI unit $\mathrm{kg}/\mathrm{m}$?

What physical quantity has SI unit $\mathrm{kg}/\mathrm{m}$? For example, the physical quantity with SI unit $\mathrm{kg}\cdot\mathrm{m}/\mathrm{s}^2$ is force $F$ and the physical quantity with SI ...
1
vote
2answers
426 views

Showing that position times momentum and energy times time have the same dimensions

I've been asked to show that both the position-momentum uncertainty principle and the energy-time uncertainty principle have the same units. I've never see a question of this type, so am I allowed to ...
19
votes
2answers
432 views

Why are expressions such as $\operatorname{ln}T$ used in thermodynamics where $T$ is not dimensionless?

In all thermodynamics texts that I have seen, expressions such as $\operatorname{ln}T$ and $\operatorname{ln}S$ are used, where $T$ is temperature and $S$ is entropy, and also with other thermodynamic ...
5
votes
1answer
142 views

Data requirement to determine proportionality

A common result of theoretical analysis in physics is some sort of relation derived from physical parameters and typically expressed in the form of a non-dimensional parameter. These scale relations ...
1
vote
1answer
177 views

Gaussian integration and dimension argument

I made a mistake recently regarding the Gaussian density, by putting the determinant of the variance to the power $\frac{d}{2}$. Would the following argumentation be valid to highlight it should be to ...
13
votes
6answers
1k views

Why isn't temperature measured in units of energy?

Temperature is the average of the kinetic energies of all molecules of a body. Then, why do we consider it a different fundamental physical quantity altogether [K], and not an alternate form of ...
2
votes
2answers
510 views

Why is the candela dimension J, not W?

According to the table at the bottom of the Wikipedia page for the candela, the dimension for candelas is J (joules). Why is this not W (watts)? The luminous intensity for light of a particular ...
0
votes
3answers
208 views

Center Of Mass Troubles

I understand the concept of Center Of Mass(com), but I am having a difficult time interpreting the equation of the simplified case of one-dimension. The book I am reading defines the position of the ...
-4
votes
1answer
102 views

Introducing dimensionality of the $+$ and $-$ signs [closed]

Is it possible to introduce some dimensionalty as $\text{kg}$ for mass or $\text{m}/\text{s}^2$ for mathematical signs: plus - $+$ and minus - $-$. The main reason of this is to avoid some common ...
0
votes
1answer
183 views

Notation for two variables with same dimensions [duplicate]

What symbol represents "has the dimensions of", as in "x has the dimensions of d"? Does such a symbol exist?
2
votes
3answers
489 views

Planck time, distance, mass? Why do we take those values?

Say we want to make an educated guess for critical values of time, distance and mass, where quantum gravity effects are supposed to be non-negligible. These values are given the prefix "Planck-". Now, ...
0
votes
2answers
144 views

Dimension analysis of de Broglie equations

One form of one of the de Broglie's equations is this: $\lambda = \frac{2\pi\hbar}{p}$ Units: $\lambda = [m]$ $\hbar = [Js]$ $p = [\frac{kg m}{s}]$ $J=[Nm]$ How can one show with dimension ...
1
vote
3answers
138 views

How could the unit of a constant be unit of tension $N^{-1}$?

From my pervious Question:What are the units of the quantities in the Einstein field equation? i noticed that the unit of this constant $\frac {G}{c^4}$ is the unit of tenstion $$\frac ...
4
votes
2answers
1k views

What are the units of the quantities in the Einstein field equation?

The Einstein field equations (EFE) may be written in the form: $$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi G}{c^4}T_{\mu\nu}$$ where the units of the gravitational constant $G$ ...
6
votes
3answers
867 views

Tips on teaching Dimensional Analysis?

What's a good way to explain dimensional analysis to a student? Here's a simple question which this method would be useful: Let's say a truck is moving with a speed of 18 m/s to a new speed of 13 ...
1
vote
4answers
376 views

Is dimensional analysis used outside fluid mechanics and transport phenomena?

Most dimensionless numbers (at least the ones easily found) used for dimensional analysis are about fluid dynamics, or transport phenomena, convection and heat transfer - arguably also sort of fluid ...
6
votes
1answer
4k views

What are the units or dimensions of the Dirac delta function?

In three dimensions, the Dirac delta function $\delta^3 (\textbf{r}) = \delta(x) \delta(y) \delta(z)$ is defined by the volume integral: $$\int_{\text{all space}} \delta^3 (\textbf{r}) \, dV = ...
6
votes
7answers
2k views

Why are radians more natural than any other angle unit?

I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
3
votes
1answer
354 views

Question about units in Lagrangian dynamics (inertia matrix)

I have a 3 degree of freedom system and my equation of motion is like this: $$M(q)q_{dd} + C(q,q_d)q_d+G(q)~=~0$$ $M(q)$: inertia matrix $C(q,q_d)$: Coriolis-centrifugal matrix $G(q)$: potential ...
1
vote
1answer
125 views

Dimensional analysis for gravitational radiation expression

on this paper, please refer to equation 2.117 for the power emitted for a rotating mass system: $$ P = - \frac{128}{5} G M^2 R^4 \Omega^6 $$ power in cgs should be (g is grams, m is meter, s is ...
0
votes
1answer
2k views

Understanding units and the units of the derivative operator

Suppose that $f$ is a function from unit $A$ to $B$, then what is the unit of $f'(x)$?. We can do $f'(x)\Delta x$ to get an estimate of $f(x + \Delta x)$. Since the latter has unit $B$, so has the ...
11
votes
5answers
2k views

How to get Planck length

I know that what Planck length equals to. The first question is, how do you get the formula $$\ell_P~=~\sqrt\frac{\hbar G}{c^3}$$ that describes the Planck length? The second question is, will any ...
3
votes
2answers
2k views

Dimensional analysis, dimensionless quantities and ratios

What justifies the "canceling out" of the same units? I have difficulty understanding the point of dimensionless quantities. Usually, when you have a concept like mass over volume, which is density, ...
5
votes
2answers
122 views

Is the “dimension” in dimensional analysis the same as the “dimension” in “three spatial dimensions”?

When we talk about the dimension of a quantity (e.g. the dimension of acceleration is$[ L \ T ^ {-2}]$) are we talking about the same "dimension" as when we talk about three dimensional space? Are ...
-1
votes
3answers
105 views

Is it possible to be changed Energy Unit in future or it is strict reality in nature?

Could you pease tell me why energy unit must be $Energy=Mass . \frac{Distance^2} {Time^2}$? (I tried to write general form of Energy unit) What is the strong proof of that unit? Does it just depend ...
2
votes
4answers
186 views

Why is the time taken for something to fall proprtional to acceleration due to gravity?

This is a continuation of this question. I saw in a piece of writing (that I no longer seem to be able to aquire) on dimensional analysis that: $$t \propto h^\frac{1}{2} g^\frac{-1}{2}.$$ How can ...
3
votes
4answers
320 views

How do I go from exponents to a formula?

This is a continuation of this question. http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/ skip this lecture to around 25:50. After doing ...
3
votes
1answer
388 views

Dimensional Analysis with $\alpha$, $\beta$, and $\gamma$ Powers

In Prof. Walter Lewin's Dimensional Analysis lecture, he stated that: $$t ~\propto~ h^α m^β g^γ$$ ($\alpha$, $\beta$ and $\gamma$ all to some power of their unit). Why does he put $h$, $m$ and $g$ ...
3
votes
1answer
296 views

How is the apparent significance of (length) scales in physics explained?

From what I understand, especially from reading arguments on Physics.SE, different (length) scales of a system are extremely important. It's clear that if there are two scales $\delta,d,D,\Delta$ with ...
1
vote
1answer
153 views

Working with atomic (?) units in solid state physics

I'm having some troubles understanding the units used in solid state physics paper. In the paper I read $\Lambda a \sim 1$ where $\Lambda$ is a momentum cutoff and $a$ is the lattice spacing of a ...
2
votes
1answer
147 views

How to interpret the appearance of time units in the units of a physical quantity?

Or phrased more abstractly, how to interpret the appearance of time dimension $[time]$ in the dimension of a physical quantity? For example, the dimension of pressure is $[mass] [length]^{-1} ...
1
vote
2answers
238 views

Dimensional analysis, fermions masses, and universal constants

I was wondering if it was possible to have a theory one day from which we will be able to derive the numerical value of the speed of light or Planck's constant. After a quick Google search the answer ...
4
votes
4answers
1k views

Can Planck's constant be derived from Maxwell's equations?

Can mathematics (including statistics, dynamical systems,...) combined with classical electromagnetism (using only the constants appearing in chargefree Maxwell equations) be used to derive the Planck ...
3
votes
3answers
876 views

What is the meaning of speed of light $c$ in $E=mc^2$?

$E=mc^2$ is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is ...
1
vote
1answer
649 views

Dimensional Analysis: Buckingham Pi Theorem Using a Matrix

I have the following problem - which is basically that $\omega = f(g,h,l)$ now the book claims that the two $\pi$ terms as follows $\pi_1 = \omega \sqrt{\frac{l}{g}}$ and $\pi_2 = \frac{h}{l}$. Now we ...
2
votes
2answers
2k views

Dimensional Analysis: Buckingham Pi Theorem

I am studying for a fluids quiz and I am having a few problems relating to dimensional analysis but for the time being fundamentally I have a problem selecting the repeating variables. Like does ...
11
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5answers
863 views

units and nature

I am wondering whether the five$^1$ units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man? Is the number of linearly independent units a ...
2
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1answer
782 views

Question Concerning Dimensional Analysis

In the first lecture of MIT's Classical Mechanics Professor Lewin talks about Dimensional Analysis.He talks about an apple being dropped from a certain height can be quantitatively expressed as the ...
3
votes
4answers
381 views

$P=ρgh$ - intuitive understanding of the equation?

I've come across this equation recently which relates pressure with the product of density, gravitational acceleration and height difference in a medium. I understand that $P = ρgh$ expands to ...
6
votes
1answer
642 views

Why can you remove the gravitational constant from a computer game simulation?

I've seen in a few gravity simulation games (ie. bouncing balls) the equation: force = G * m1 * m2 / distance^2 shortened to this by removing the gravitational ...
13
votes
8answers
1k views

In dimensional analysis, why the dimensionless constant is usually of order 1?

Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1. What ...
10
votes
5answers
1k views

Dimensional analysis restricted to rational exponents?

After some reading on dimensional analysis, it seems to me that only rational exponents are considered. To be more precise, it seems that dimensional values form a vector space over the rationals. My ...
20
votes
11answers
6k views

What is the logarithm of a kilometer? Is it a dimensionless number?

In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is. Suppose I have something with length $L = 1 km$. $\lg L = \lg km$ It ...
8
votes
2answers
2k views

Why are smaller animals stronger than larger ones, when considered relative to their body weight?

I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat. It has been suggested to me that this is due to ...
5
votes
1answer
323 views

Deriving or justifying fundamental constants

Is there a fundamental way to look at the universal constants ? can their orders of magnitude be explained from a general points of view like stability, causality, information theory, uncertainty? ...
1
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2answers
5k views

Dimensonal analysis of damping constant?

What are the units of the damping constant from the following equation by dimensional analysis? $$\zeta = \frac{c}{2\sqrt{mk}}$$ I'm assuming the units have to be s^-1, as the damping constant is ...