Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

This tag is for questions on the mathematics required to solve problems in physics and should not be confused with those on physics concepts. Pure physics questions should go in the Physics Stack Exchange. For questions in the field of mathematical physics, please use the tag instead.

5372 questions
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Is there such thing as a "smallest positive number that isn't zero"?

My brother and I have been discussing whether it would be possible to have a "smallest positive number" or not and we have concluded that it's impossible. Here's our reasoning: firstly, my brother discussed how you can always halve something, $(1,…
user361319
32
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2 answers

Perfectly centered break of a perfectly aligned pool ball rack

This question is asked on Physics SE and MathOverflow by somebody else. I don't think it belongs there, but rather here (for reasons given there in my comments there; edit: now self-removed). Imagine the beginning of a game of pool, you have 16…
Řídící
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What mathematical structure models arithmetic with physical units?

In physics we deal with quantities which have a magnitude and a unit type, such as 4m, 9.8 m/s², and so forth. We might represent these as elements of $\Bbb R\times \Bbb Q^n$ (where there are $n$ different fundamental units), with $(4,…
MJD
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How does one parameterize the surface formed by a *real paper* Möbius strip?

Here is a picture of a Möbius strip, made out of some thick green paper: I want to know either an explicit parametrization, or a description of a process to find the shape formed by this strip, as it appears in the picture. Now before you jump up…
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Why does adding a term $5f'(t)$ to $5f''(t)+10f(t)=0$ cause damping?

So we have a differential equation to model an oscillator: $$5f''(t)+10f(t)=0$$ Where the initial conditions are $f(0)=0$ and $f'(0)=4$. It is given that $f(t) = \frac{2\sqrt 2}{5}\sin\sqrt2 t$. Now, if we make make a slight change to the original…
27
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1 answer

Density and dimensionality of zeros in inverse square force fields of randomly distributed sources in (at least) 1, 2 and 3 dimensions?

Background: In this answer to Are there places in the Universe without gravity? in Astronomy SE I did a quick finite 2D calculation for 20 random sources to see if there was at least one zero, and without rigor convinced myself that there might…
uhoh
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Making a standard theoretical physics argument rigorous

In theoretical physics one often encounters the following rationale: if $f$ and $g$ are functions on $\mathbf{R}^n$, satisfying some technical conditions, and $\displaystyle\int_\Omega f=\int_\Omega g$ for all open sets $\Omega$, then $f=g$. (For…
26
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Does Gödel's Incompleteness Theorem really say anything about the limitations of theoretical physics?

Stephen Hawking believes that Gödel's Incompleteness Theorem makes the search for a 'Theory of Everything' impossible. He reasons that because there exist mathematical results that cannot be proven, there exist physical results that cannot be proven…
Haskell Curry
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26
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Why does dust gather in corners?

I've noticed when sweeping the floor that dust gathers particularly in the corners. I assume there is a fluid mechanics reason for this. Does anyone know what it is? Edit: No, really, this is a mathematical question. Air blows around the room,…
isomorphismes
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Atiyah's definitions of Topological Quantum Field Theory

According to Atiyah, a TQFT is a functor from the category of cobordisms to the category of vector spaces. How does this definition relate with the physics of quantum mechanics? What does the category of cobordism in the above definition represent…
24
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What is the exact and precise definition of an ANGLE?

On wikipedea I found a definition of an Angle as such: "In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the arc…
user103816
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Calculate moment of inertia of Koch snowflake

That's just a fun question. Please, be creative. Suppose having a Koch snowflake. The area inside this curve is having the total mass $M$ and the length of the first iteration is $L$ (a simple equilateral triangle of side $L$). Assume the density…
Blex
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Why is this allowed? ("Fourier's Trick"; finding the coefficients in a Fourier Series)

In my textbook (Introduction to Electrodynamics, D. Griffiths), we derive the equation for some strange potential function. Eventually, we get to this (for $n \in \mathbb{Z}^+$): $$ V_0(y) = \sum_{n=0}^{\infty} C_n\sin{\frac{n\pi}{a}y}…
AmagicalFishy
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What Mathematics questions can be better solved with concepts from Physics?

Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics questions you've found that can be better solved with a…
Vincent Tjeng
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What does the integral of position with respect to time mean?

The integral of acceleration with respect to time is velocity. The integral of velocity with respect to time is position. What is the integral of position with respect to time, and what does it mean? Please explain so that your answer is…
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