# Questions tagged [dimensional-analysis]

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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### 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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### Why *should* the mass of elementary particles theoretically be of the magnitude of the Planck mass?

Why should the mass of elementary particles be theoretically of the magnitude of the Planck mass? I've read that already a few times but I don't understand why it should be that way. For example: ...
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### 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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### How does the Fourier Transform invert units?

I don't really understand how units work under operations like derivation and integration. In particular, I am interested in understanding how the Fourier transform gives inverse units (i.e. time ...
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### Meaning of dimension in dimensional analysis

I was wondering what dimension can mean in physics? I know it can mean the dimension of the space and time. But there is dimensional analysis. How is this dimension related to and different from the ...
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### Simple Harmonic Motion - What are the units for $\omega_0$?

I'm trying to understand the units in: $$mx''+kx=0$$ And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$ Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring ...
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### 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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### 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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### 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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### 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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### 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\ ...