# 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.

117 questions
Filter by
Sorted by
Tagged with
11k views

### 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 ...
32k views

7k 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 $G$ ...
2k views

### What is the justification for Rayleigh's method of dimensional analysis?

It seems to me that although dimensional analysis is useful for demonstrating when a physics equation is wrong (when the dimensions are inconsistent), there is little justification for how it is often ...
775 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? ...
5k views

### Is speed of light and sound rational or irrational in nature?

Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ? I'm talking about ...
10k views

### Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
383 views

### Why are the anthropometric units (which are about as big as we are) as large as they are relative to their corresponding Planck units? [duplicate]

This might have some duplicated inquiry that this question or this question had, and while I think I have some of my own opinions about it, I would like to ask the community here for more opinions. ...
426 views

### Estimating the yield of the Trinity Test using dimensional analysis

So essentially I'm trying to re-do what G.I. Taylor did to estimate the energy released by the Trinity Test using dimensional analysis. I understand all of the dimensional analysis aspects, I'm just a ...
360 views

### Confusion With How Dimensions Work

Form what I understand if you have an equation such as: $$v = v_0 + at$$ then the dimensions must match on both sides i.e. $L/T = L/T$ (which is true in this case), but I have seen equations such as ...
767 views

### Why is the string length around the Planck length?

In string theory, it is assumed that a string is about the size of a Planck length, $$\ell_{string} \sim \ell_{Pl} \simeq 10^{-35}\,\text m.$$ Why that length? Why not for example a hundred times ...
9k views

### Why do we assume, in dimensional analysis, that the remaining constant is dimensionless?

Walter Lewin's first lecture (at 22:16) analyzes the time $t$ for an apple to fall to the ground, using dimensional analysis. His reasoning goes like this: It's natural to suppose that height of the ...
19k views

7k views

### What does the decay constant mean?

In my curriculum, the decay constant is "the probability of decay per unit time" To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a ...
652 views

### A simple explanation of Kepler's Third Law

Is there a simple way to explain how Kepler's third law follows from the inverse square law that of gravity (and laws of motion) For example for Kepler's second law we can say it's because Gravity ...
943 views

### Is the number 1 a unit?

In dimensionless analysis, coefficients of quantities which have the same unit for numerator and denominator are said to be dimensionless. I feel the word dimensionless is actually wrong and should be ...
2k views

### Units inside a logarithm

I have troubles understanding a seemingly simple integral in a physical context. Take a look at $\int_{V_1}^{V_2} \frac{\mathrm{d}V}{V}$ which appears in isothermal expansions (V being the volume of a ...
4k views

### Why aren't trigonometric functions dimensionless regardless of the argument?

Consider this equation :- $$y = a\sin kt$$ where $a$ is amplitude, $y$ is displacement, $t$ is time and $k$ is some dimensionless constant. My instructor said this equation is dimensionally ...