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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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 ...
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1answer
160 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} ...
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2answers
259 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 ...
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4answers
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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 ...
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3answers
924 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 ...
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701 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 ...
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2answers
3k 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 ...
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5answers
896 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 ...
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1answer
868 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 ...
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4answers
414 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 ...
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1answer
711 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 ...
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8answers
2k 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 ...
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5answers
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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 ...
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11answers
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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 ...
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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 ...
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1answer
355 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? ...
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2answers
6k 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 ...
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3answers
891 views

How can I understand counterintuitive units like $\text{s}^2$?

One of the things I never understood, but was too afraid to ask is this: how should I think of things like $\frac{\text{kg}}{\text{s}^2}$. What exactly is a square second? Square foot makes sense to ...
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2answers
1k views

How does the period of an hourglass depend on the grain size?

Suppose I have an hourglass that takes 1 full hour on average to drain. The grains of sand are, say, $1 \pm 0.1\ {\rm mm}$ in diameter. If I replace this with very finely-grained sand $0.1 \pm 0.01\ ...