# Questions tagged [geometry]

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

635 questions
Filter by
Sorted by
Tagged with
87 views

### Unit Vectors in physics

I'm reading the Massachusetts Institute of Technology: "Review of Vectors" , and I've found this: I can't see any relationship between the text that is highlighted in yellow and what's depicted in ...
76 views

### Scaling of mass density

Let distances scale as $L'=kL$, $k$ is the scaling factor. Then spherical volume will scale as $V'=k^3 V$. Say, the sphere is filled with mass with constant density. If we scale the model with ...
46 views

### Rotor finds equilibrium in TWO positions, why and how?

I have a Mendocino motor, a toy with magnets, solar panels, and coils. Such a thing requires careful balancing (eg. with tiny bits of tape) to achieve sufficient balance that it will start rotating ...
30 views

### Computing length of a closed path given a spatial metric

I'm trying to self-study the "cosmology" chapter in Gravitation and Spacetime By Hans C. Ohanian and Remo Ruffini, and I'm stuck on the wording in problem 9.6: The spatial line element for a ...
76 views

### Geometrized Algebra and Einstein's Equations

The algebraic properties of the pseudoscalar $i$ follows the ordinary rules for imaginary numbers: So its algebraic properties are ~ $i^2 = -1$ the amazing geometric property is that it is an ...
132 views

### Unlike rotation, why a $3\times 3$ translation matrix cannot be written in 3D? or can it be?

The effect of rotation in 3d on a vector, $\vec{r}=x\hat{x}=y\hat{y}+z\hat{z}$ is given in the form a matrix product:$$\vec{r}\to O\vec{r}$$ where $O$ is a $3\times3$ proper orthogonal matrix. Can we ...
54 views

### How to interpret Einstein's development of Euclidean orthogonal transformations in The Meaning of Relativity?

My questions pertain to the development of Euclidean 3-space orthogonal transformations presented in Einstein's The Meaning of Relativity. Also available at https://en.wikisource.org/wiki/...
3k views

### Why do water drops form spheres in space? [duplicate]

When water is poured out in space, why does it always take a spherical ball-like shape?
43 views

### Is 1/vector is a vector or not? [duplicate]

Let $\vec { A } = a \hat { i } + b \hat { j } + c \hat { k }$. Is $\frac { 1 } { \vec { A } }$ a vector or not, and if it is, then what are its components?"
241 views

### How can Young modulus depend on the geometry of the item & Lennard Jones (question related to an older one)

In the question Young's modulus and geometry of test material, the answer was that it cannot play any role. Nonetheless, for the Lennard-Jones solid, in many places the Young modulus is given as : ...
544 views

### Linearizing the Einstein-Hilbert action; shortcuts?

I am interested in linearizing actions that are constructed out of geometrical objects. By this I mean perturbing the metric (or vielbein) and keeping in the action terms which are quadratic in the ...
244 views

### Rindler Metric and Minkowski metric

I am trying to understand why the Rindler Metric line-element and Minkowski metric line-element represent the same spacetime. Could someone help me understand that?
131 views

### How to specify the orientation of an area vector?

We all know that the area of a triangle having consecutive sides as $\vec { a }$ and $\vec { b }$ is $\frac { 1 } { 2 } | \vec { a } \times \vec { b } |$, but what is the direction of that area vector?...
63 views

42 views

### Could every particle encode the distances to all other particles?

I was thinking about quantum gravity and pre-geometry and wondering this question: "If space does not exist. How does a particle know how far away it is from another particle?" i.e. there are no ...
223 views

### What is the diameter size of the umbra shadow cone of the Earth when the Moon passes through it on a lunar eclipse?

I am sure this varies given the distance from moon to earth varies, but a range would be sufficient. I am trying to explain to a flat earther how there is not a lunar eclipse every full moon. My ...
61 views

### Does a circle become bigger or smaller when rotating? [duplicate]

Say a circle is rotating about its centre at a relativistic speed. If it were not rotating in your reference frame, its circumference divided by its diameter would be $\pi$. Now, because it is ...
250 views

### (I-beam vs rectangular beam) Which sword blade cross section is less likely to break?

Original question Assumption: i made several swords with different cross sections (lenticular, single broad fuller as in viking swords, diamond, hollow ground diamond) the blades are made using the ...
33 views

### Spacing of atoms in a cubic meter [closed]

I want to figure out the spacing between neighbouring atoms in a cubic meter of a large amount of 10^17 atoms were placed in perfect cubic structures within the cubic meter. I’m not sure how to go ...
117 views

### Calculating the Earth-Sun distance

Using just the facts that the period of earth around the sun is 1 year. that the distance of 1 degree of latitude on earth is 100km . that the acceleration due to gravity on earth is 10m/s^2 and that ...
146 views

### How can momentum and position be combined into a phase space when they have different units?

Elaboration of the question: What is the geometrical interpretation of units? As in, a unit of length is a choice of scaling of the coordinate systems i.e. it is a choice of diffeomorphism, but then ...
64 views

### What is Snell's law's main formula?

My book states it as $(\sin i)/(\sin r)=n$. However, University Physics has a different say. It says, $n_{a} \sin a =n_{b} \sin b$. Which of the following is correct?
146 views

### Spinors in Classical Mechanics and Geometry?

I'm trying to deepen my understanding of spinors by looking at applications in simple problems, preferably unrelated to quantum mechanics. For this purpose I'd like to refrain from discussing ...
121 views

### Living at the equator (Colombia), how to figure out the orientation towards north using the sun falling through a window?

The real life issue is this: A friend is moving to a new apartment. What is bad here, is if the apartment is getting full sun in the morning or afternoon. So the Sun goes from east to west, right? If ...
184 views

### Generalized Formula for Interference Maxima & Minima of Circular Waves

Consider two point sources which generate circular wave disturbances (e.g. speakers, radio towers, etc.) which propagate uniformly in all directions. Provided that each source emits its signal in-...
81 views

### Can one of the component of a vector have the same magnitude of the vector? [closed]

In vectors, if a vector is broken down into its components then can one of the components of the vector have the same magnitude of the vector itself??
147 views

### Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
46 views

### Defining the change in direction due to wind

My question: Which force vector (A, B, C, or D) represents the APPROXIMATE direction in which the boat is travelling as a consequence of the wind? My approach: I looked for which vector combination ...
53 views

### Uncertainty when a measurement is given as “between this number and that number”

A regulation soccer field for international play is a rectangle with a length between 100 m and 110 m and a width between 64 m and 75 m. It then asked me to calculate the area which is easy but I don'...
114 views

### Irrep corresponding to a rotation, what's the definition?

My character tables for point group $T$(Schönflies-notation but easily convertible into other point group notations) tell me that the rotation around the $z$-axis, $R_z$ (the $z$-direction ...
404 views

### Tension between two/three ropes using vectors

Say there are three points, $a$, $b$, and $c$, with associated vectors $\vec{r_a}$, $\vec{r_b}$, and $\vec{r_c}$. $a$ and $b$ are both attached to firm surfaces, and each are connected to $c$ by ideal ...
67 views

### Electric Potential Energy in $0$ space like dimensions and $t$ time like dimensions in the case of massive photons

Several months ago I asked about electric force in higher dimensions in the case of massive photons What would be the force law for the electric force between two electric charges in higher dimensions ...
77 views

### Do we see an ellipse when we view Earth's horizon?

I wanted to try to determine mathematically exactly how much curvature one should see on the horizon when I viewed it from a given height, and it hit me that looking at the horizon is not the same as ...
65 views

### What does it mean to find the component of 2 vectors in the direction of another vector?

I understand how to take the cross-product of 2 vectors ($\vec{a}\times\vec{b}$), but what does it mean to find the component of $\vec{a}\times\vec{b}$ along the direction of another vector (for ...
113 views

### For a disk within a ring, why is arclength proportional to $R*\theta$ but not $a*\phi$?

Here is an example problem, why is $\phi$ not by itself in the constraint equation? Can someone explain this geometrically? It seems like the curve of the surface curves away from the disk, but that ...