# 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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### Why is contact resistance measured in $\Omega~\mu m$?

In many papers the contact resistance of a metal in contact with a semiconductor is given in units of $\Omega~\mu m$, for example in the paper by Li et al. (Appl. Phys. Lett. 102 (2013), p. 183110): ...
1answer
91 views

### What makes a system of units self-consistent?

What are the rules governing the creation of a self-consistent system of units? To be clear, I'm not asking about making units universal or replicable, I'm asking about the mathematics governing what ...
1answer
204 views

### What is the difference between physical dimensions and physical quantities?

What is the difference between physical dimensions and physical quantities if the dimension of mass is also mass?
1answer
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### Notation for feet and inches dimension

I am looking at a set of construction plans where all the dimensions read as x' - y". One example would be 4' - 6". I am confused by the dash in between the feet and inches. Is this supposed to mean ...
2answers
74 views

### Super confused over simple unit conversion from centimeters to cubic centimeters

I'm stuck in a really stupid question. It seems like the meaning of "centi" is chancing meaning. Because if: $r = 5 cm = 5 \cdot 10^{-2} m$ so $c = 10^{-2}$ But say i need to take the cubic root ...
4answers
215 views

### Is the fine-structure constant related to the size of the observable universe?

The fine-structure constant $\alpha \approx 1/137$. In Planck units, this is also the charge of the electron squared, $e^2 = \alpha$ ($e \approx 0.085$). In Planck units the size of the observable ...
4answers
262 views

### How does natural unit make sense? [duplicate]

Both the fundamental constants $\hbar$ and $c$ have dimensions. In particular, $[\hbar]=ML^2T^{-1}$ and $[c]=LT^{-1}$. But in natural units, we make them dimensionless constants of equal magnitude. ...
2answers
65 views

### About the dimension of the SI units vector space

We know that the set of fundamental and derived physical units can be structured as a vector space over the rational numbers. In the International System of Units the dimension of this space is $7$ ( ...
2answers
64 views

### When is the order of magnitude not equal to the exponent of scientific notation?

Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
1answer
112 views

### When do you use Quantum Mechanics? [duplicate]

Given a problem, how does one know whether to use quantum mechanics or classical mechanics? Take for example electron scattering from a nucleus. The electrons are given a wavefunction in this case. ...
3answers
159 views

### Where is the line between Quantum and Relativity?

Its often said QM is for the very small and GR for the very large. This brings to mind that there should be some limit at which one starts to apply and the other stops. Now I know there are more ...
2answers
178 views

### Dimensions of mass in terms of Length and Time

From Maxwell's Treaties on Electricity and Magnetism: For acceleration due to attraction of a mass m at a distance r is by the Newtonian Law m/(r^2). Suppose this attraction to act fro a very small ...
1answer
93 views

### Hydrodynamic interaction between two spheres in $Re\ll 1$ flow

I am studying the interaction between two spherical particles of radius $a$ in a low Reynolds number flow. Because of linearity, I know that their respective velocities will be linear in the forces ...
1answer
83 views

### A question about natural/geometrized units

I had a question about the following document- Natural units I understand the conversion factors. But if you look at the tables, they take an SI unit, say 1 kg, convert it into geometrized units, say ...
2answers
52 views

2answers
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