The dimensional-analysis tag has no wiki summary.
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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 ...
7
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5answers
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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
233 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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9answers
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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 ...
12
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5answers
944 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 ...
8
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3answers
557 views
Understanding counterintuitive units like s^2
One of the things I never understood but was too afraid to ask is this: how should I think of things like kg/s^2. What exactly is a square second? Square foot makes sense to me because I can see it, ...
3
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1answer
201 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 ...
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7answers
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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 ...
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2answers
338 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 $G$ ...
3
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4answers
297 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
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1answer
246 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 $g$ ...
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1answer
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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} ...
