Questions tagged [geometry]

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

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2answers
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 ...
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1answer
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 ...
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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 ...
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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
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 ...
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2answers
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 ...
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0answers
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/...
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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
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?"
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1answer
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 : ...
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1answer
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 ...
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2answers
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?
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3answers
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?...
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1answer
63 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
88 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
466 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
133 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
235 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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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 ...
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1answer
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 ...
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0answers
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 ...
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1answer
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 ...
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0answers
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 ...
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1answer
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 ...
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2answers
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 ...
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1answer
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?
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0answers
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 ...
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1answer
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 ...
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1answer
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-...
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3answers
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??
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1answer
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?
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1answer
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 ...
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1answer
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'...
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1answer
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 ...
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2answers
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 ...
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0answers
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 ...
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2answers
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 ...
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2answers
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 ...
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2answers
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 ...
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1answer
83 views

A geometrical calculation in Fresnel's paper “Memoir on the diffraction of light” 1819

It is a geometrical problem which I find difficult to solve reading the Fresnel's paper "Memoir on the diffraction of Light". According to the figure Fresnel sets $z$ as the distance of the element $...
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0answers
27 views

Angular diameter of a particle outside of the observable universe?

"Angular diameter" and "apparent size" seem to be used interchangeably in cosmology. But if an object is outside of the observable universe, then isn't it no longer "apparent", yet it would still have ...
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5answers
925 views

What does it mean if the dot product of two vectors is negative?

If the dot product gives only magnitude, then how can it be negative? For example, in this calculation: $$W = \vec{F}\cdot\vec{r} = Fr\cos\theta = (12\ \mathrm{N})(2.0\ \mathrm{m})(\cos 180^\circ) = ...
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1answer
986 views

Definition of impact parameter

David Morin defines impact parameter as: which is the semi minor axis of the conic. But according to Wikipedia and some other sources: It is the perpendicular distance from the center of potential ...
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1answer
128 views

What is the actual meaning of dot product of 2 vectors? [duplicate]

I couldn't get the physical significance of dot product
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2answers
1k views

When will velocity and acceleration vectors be perpendicular? [closed]

Suppose a particle is moving in the $xy$ plane with $$x=at, \quad y=at(1-bt),$$ where $a$ and $b$ are positive constants. When will the velocity vector and acceleration vector be perpendicular? I ...
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1answer
34 views

Form of a mass to exert constant gravitational pull over a non-trivial path?

When an apple falls from a tree, Earth exerts a gravitational pull on the apple that amounts to an acceleration of around $9.81\,m/s^2$. But as the apple falls, it gets closer to Earth and thereby the ...
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1answer
45 views

How to stack padding materials to pad an edge [closed]

This is about how to combine materials of various elastic and deformation properties as a stack to show different properties as a stack. A cardboard box has two holes punched in the side of the box ...
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2answers
141 views

Velocity vector for helical motion? [closed]

Problem describes a point particle moving in an upwards helix, with the velocity in the $z$-direction being a constant 3 m/s and circular uniform motion in $xy$-plane along a circle with radius = 6 m ...
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0answers
322 views

Calculating the Gaussian Curvature of Cylinder

In the book "Gravitation" by Misner, Thorne and Wheeler, exercise 1.1 on page 44 reads: Show that the Gaussian curvature $R$ of the surface of a cylinder is zero by showing that geodesics on that ...
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2answers
951 views

How do I find the longitude of the subsolar point? [duplicate]

On December 21, 2018 at 2:23pm PST I want to be standing as directly under the sun as humanly possible. Obviously the latitude of that point will be the Tropic of Capricorn. Assuming I have the right ...

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