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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Are units of angle really dimensionless?

I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've ...
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What justifies dimensional analysis?

Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular ...
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Dimensionless Constants in Physics

Forgive me if this topic is too much in the realm of philosophy. John Baez has an interesting perspective on the relative importance of dimensionless constants, which he calls fundamental like alpha, ...
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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 $L = 1 km$. $\log L = \log km$ ...
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In dimensional analysis, it does not make sense to, for instance, add together two numbers with different units together. Nor does it make sense to exponentiate two numbers with different units (or ...
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What do units like joule * seconds imply?

I can easily understand what divisive units imply, but not what multiplicative units imply. What I mean is, when I read "$12 \:\mathrm{eggs/carton}$", I mentally convert it to, "There are 12 eggs ...
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Do all equations have identical units on the left- and right-hand sides?

Do all equations have $$\text{left hand side unit} = \text{right hand side unit}$$ for example, $$\text{velocity (m/s)} = \text{distance (m) / time (s)},$$ or is there an equation that has different ...
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Why are angles dimensionless and quantities such as length not?

So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths. Ok so far, so good. Then came the question: ...
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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 ...
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Why is it natural to look for solutions involving dimensionless quantities?

While studying the Heat Equation, I got stuck in a statement in my book. It says: We have seen that the combination of variables $\displaystyle \frac{x}{\sqrt{Dt}}$ is not only invariant with ...
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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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Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...
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Is it possible to speak about changes in a physical constant which is not dimensionless?

Every so often, one sees on this site* or in the newsâ€  or in journal articlesâ€¡ a statement of the form "we have measured a change in such-and-such fundamental constant" (or, perhaps more commonly, "we ...
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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 ...
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 ...