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Questions tagged [geometry]

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

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58 views

Can’t we use ‘vector product’ to find the angle between two vectors? [migrated]

There are two vectors : $A = (\hat i + j + k)$ and $B = (\hat i - \hat j - \hat j)$, where $\hat i$, $\hat j$, and $\hat k$ are unit vectors along $x$, $y$, and $z$ axis respectively. We have to find ...
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0answers
26 views

Intuition for orientation of tri-vectors in geometric algebra [migrated]

I am learning geometric algebra from the MacDonald textbook and it states that the outer product is associative. Letting $\bf{u}$, $\bf{v}$, and $\bf{w}$ be vectors $$\bf{u} \wedge \bf{v} \wedge \bf{...
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1answer
31 views

Why should the position vector be noted as $R\hat{R}$ in spherical polar coordinates?

Why should the position vector be noted as $R\hat{R}$ in spherical polar coordinates? Now i did the calculation like this: $\vec R = R \sin\theta \cos\phi \hat{i} + R \sin\theta \sin\phi \hat{j} + R \...
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0answers
66 views

Derivation of $\frac{\cos(\theta)dA}{r^2} = d\omega$ [on hold]

Note: I asked the same question on the mathematics stackexchange, but was advised to ask it here. It also seems to arise quite often in physics. I've been looking for a (formal) derivation of the ...
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2answers
43 views

Deriving density of states in different dimensions in k space

The results for deriving the density of states in different dimensions is as follows: 3D: $g(k)dk = 1/(2\pi)^3 4 \pi k^2 dk$ 2D: $g(k)dk = 1/(2\pi)^2 2 \pi k dk$ 1D: $g(k)dk = 1/(2\pi) 2 dk$ I get ...
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0answers
29 views

Soft question: Discrete mathematics or geometry for theoretical physics [closed]

I am currently studying physics at university and I want to specialise in theoretical physics. I love mathematics but I am not sure what maths courses are best for theoretical physicists? More ...
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3answers
97 views

The direction of torque is so confusing [duplicate]

When I was studying cross and dot products, I learned that the cross product of two vectors A and B is perpendicular to both A and B. But my mind is unable to understand that. Since both A and B are ...
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0answers
30 views

Looking for a geometric cosmology model where time behaves like an orientation

This question is literally inspired from seeing the above scene unfold. Let the merging and splitting light spots you saw in the above gif be pairs of particles and anti particles, let the shape of ...
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0answers
40 views

Geometric Surface-to-volume ratios

Is there any physical or scientific significance for the fact that an inscribed sphere in a regular tetrahedron have exactly the same surface to volume ratio at any size?, (i.e. does it have any use ...
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1answer
48 views

Supplementary quantities in physics [closed]

Why are supplementary quantities, namely solid angle and plane angle, placed separately in physics apart from derived and fundamental quantities? https://www.tek.com/service/metrology/fundamentals-...
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2answers
81 views

Are trigonometric ratios physical quantities or not [closed]

Are trigonometric ratios like $sin$, $cos$, $tan$, etc. physical quantities in physics? I know that angles like plane angle and solid angle are derived quantities in physics but are $sin()$, $cos()$,...
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1answer
47 views

Is there a way to separate 2D from 3D? [closed]

When we see object around us in space, we can always interpret those in 2D, by considering them to pass through a plane, its only when we interact with those objects do we realise that it is 3D, is ...
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0answers
27 views

What is the simplest way of getting the solid angle $\Omega_d$ in a space of $d$ dimensions? [migrated]

It is known that the solid angle in a flat space of $d$ dimensions ($d = 2 n$ or $d = 2 n + 1$) is given by these formulae: \begin{align}\tag{1} \Omega_{2 n} &= \frac{1}{(n - 1)!} \, 2 \pi^n, \...
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0answers
19 views

Need an equation to calculate the list of latitudes and longitudes of an off-nadir sensor with a given half angle

I need a deterministic way to determine a list of latitude and longitudes of an off-nadir pointing sensor for a given half angle. Below is a depiction of the problem. It isn't too hard to calculate ...
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2answers
64 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 ...
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1answer
17 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 ...
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0answers
39 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 ...
1
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1answer
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 ...
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1answer
38 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 ...
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2answers
127 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 ...
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0answers
47 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/...
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1answer
60 views

Vehicle Dynamics Problem: Cornering wheels must slide on the road [duplicate]

Can anyone see this geometric fact that cornering wheels must slide on the road? What I mean is that the tread within the contact patch of the rolling wheel, which is travelling along a curved/...
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3answers
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?
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0answers
40 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?"
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1answer
40 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 : ...
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1answer
76 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 ...
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2answers
79 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?
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3answers
65 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?...
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1answer
55 views

Integration Using Spherical Coordinates [closed]

So I had to find the moment of inertia of a hollow sphere of mass $M$, radius $R$, and negligible thickness. $dI=R^2 \cdot dm$ where $dm = \dfrac{M}{4\pi R^2}\cdot R^2\sin(\theta)\cdot d\theta\cdot ...
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1answer
68 views

Calculate launch angle of object moving away from view

I'm writing image processing software and my goal here is to take an image of a projectile moving away from the camera and determine the launch angle. What I already know is: The actual size of the ...
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3answers
243 views

Extracting the 3D coordinates of a moving object from a video

Take a look at these two pictures, which are stills from a video which demonstrates magnus effect in football: I want to extract the coordinates of this ball in 3D space from this video. These are ...
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1answer
43 views

Unit vector in displacement

When we use vectors in physics why does the unit vector (for displacement) equals magnitude of 1 or magnitude of 1m?
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5answers
161 views

Why we use vectors?

When we say that the position of an object is +5m on x axis why we need to use vectors? I mean could we don't use vectors and just say +5m on x or y or z axis instead of writing 5*unit vector either $...
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0answers
37 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 ...
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1answer
37 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 ...
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0answers
60 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 ...
3
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1answer
98 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 ...
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0answers
28 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 ...
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1answer
67 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 ...
4
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2answers
94 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 ...
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1answer
52 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?
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0answers
61 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 ...
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1answer
48 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 ...
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1answer
49 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-...
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3answers
66 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??
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1answer
60 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?
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1answer
30 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 ...
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votes
1answer
37 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'...
2
votes
1answer
80 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 ...
1
vote
2answers
91 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 ...