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

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Generators of cubic group: Euler angles

I am trying to build numerically all members of the cubic group in the representation of Wigner D matrices. Angular-momentum quantum number may be small, e.g. 2, so I use the formula stated e.g. at ...
2
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4answers
64 views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
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2answers
84 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
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0answers
32 views

Geometric meaning of negative triple product [migrated]

Create a tetrahedron with corners $A=(1,2,4)$, $B = (1,0,2)$, $C = (2,1,3)$ and $D = (4,1,1)$. Determine the angle $\alpha$ between the edge $AB$ and the side $BCD$. The first step I make is ...
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1answer
64 views

If the Earth were a pool ball, could I feel mountains? [on hold]

If the earth (12,742 km diameter) were scaled down to the size of a pool ball (61mm diameter), the mountain ranges would still exist, obviously. But would a typical human be able to feel those ...
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3answers
256 views

What is the difference between the shapes of molecules with different isotopes

I'll explain my question on example of water molecule. Let us have three water molecules: normal water $H_2 O$, heavy water $D_2 O$ and semiheavy water $HDO$. Is there any difference between the ...
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1answer
115 views

How do you compute for the center of a rotation of a bicycle?

I know how to find the center of a rotation, like where you connect the side and make bisector with the help of your compass. But in a situation like this how do I get the $a_2$? I'm doing an advance ...
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1answer
43 views

Finding angle between two displacements [closed]

Consider two displacements, one of magnitude 6 m and another of magnitude 8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 14 m, (b) 2 m, ...
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53 views

Feynman lectures, Volume I, chapter 13-4 [migrated]

While reading Feynman lectures on Physics, volume I, Chapter 13-4, I found following assumption, which I don't understand: Then, since $r^2 = \rho^2 + a^2$, $\rho\,d\rho = r\,dr$. Therefore ... ...
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0answers
17 views

Resistance of geometric shapes to torque [closed]

Would a box shape A) 155 meters by 25 meters by 15 meters have a greater resistance to torque than a box shape B) 140 meters by 15 meters by 9 meters. If so, why? My intuition is that Shape A would ...
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1answer
153 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
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2answers
487 views

Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
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4answers
180 views

Bicycle counter-intuitive: in which direction it will move? [duplicate]

I saw this puzzle in a local newspaper: Consider a normal bicycle set to stand in its upright position, and its pedal is set to the position as shown in this figure. One man slightly hold the ...
2
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2answers
131 views

How many are the points which are $n$th nearest to a certain point in a hexagonal lattice

Suppose there are infinite points arranged as hexagonal lattice. The question is the one as the title. First we choose a point called $A$. Then when we count the $n$th nearest points to $A$, what ...
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0answers
25 views

Terminology - optical (visual) properties of a structure

I am trying to understand few terminological problems that I encounter. Without knowing keywords it is hard to perform search for literature or publications in the area. The area relates to the ...
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0answers
36 views

The Ehrenfest Paradox and Euclidian Assumptions [duplicate]

As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that "the radius doesn't undergo Lorentz contraction", ...
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1answer
348 views

Area moment of inertia of regular $n$-gons over polygon center $O$

Is it possible to consider the regular polygons ($n$-gons) as deformed circles and use a pseudo-polar coordinate system to calculate their moment of inertia over its center $O$. Inasmuch as I know (I ...
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0answers
24 views

Snyder's Lorentz invariant discrete space-time

Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous? I'm sure this has been ...
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2answers
16k views

Finding the drag force (Air resistance force) for accelerated ball?

As you know if I want to find the force for an accelerated object I will use the law $F_o=ma$ so I can get the affecting force of it. But there is another force affecting against the object. It's the ...
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1answer
30 views

Determining Height of Platform on Fulcrum

Consider this scenario: We have a platform resting on a fulcrum. The platform's tilt is controlled by a motor attached to 2 levers: Is the link between the height of the top of the lever ...
1
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1answer
35 views

The relationship between abstract geometrical concepts and reality? [closed]

In pure geometry points have no parts, lines no breadth and surfaces no thickness, geometrical figures can be exactly congruent. But how do these concepts relate to the physical world. What is the ...
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0answers
45 views

Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
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11answers
2k views

Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
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2answers
62 views

Relative motion of an arbitrary volume of space ( is space static or dynamic?) [closed]

Do physicists consider space as being "static" or "dynamic" ? Hi I asked a question about whether space can move, and from the answer, I realized I was not precise enough and did not actually ask ...
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1answer
50 views

3D donuts and the centre of a black hole [closed]

I have been trying to imagine ways to visualise the gravitational field of the earth... It's near zero at the outer edges of the atmosphere, strong at sea level, strongest at the quarter point, then ...
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2answers
963 views

Triple-right triangle experiment: what's the minimum distance?

As I had showed in a previous answer, among the other ways to prove that the Earth is round, we have the triple-right triangle. The idea is simple: Starting from point A you move in a straight ...
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1answer
61 views

When is a circle not a circle?

Imagine a 2D uniform circular motion of constant magnitude but changing direction in an area of zero g. The forces will be equal all the way round - it will be a perfect circle. Now imagine the same ...
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6answers
3k views

Gravitation is not force?

Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and ...
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0answers
14 views

Angular current in torus

I'm trying to find the magnetic field due to a torus anywhere in space. I'm approximating it as a circular current loop. What I'm having a hard time with is the current in the theta direction, that ...
4
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0answers
141 views

Can space move? [closed]

I have some questions; I hope you don't mind: $\bullet$ If the space between two distance galaxies is increasing, then is the volumes of space in which the galaxies find themselves also moving apart? ...
3
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4answers
127 views

Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
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4answers
75 views

Proving that the Center of Mass of a solid sphere is at the origin [closed]

For my own knowledge and to understand why. I am trying to convince myself that the center of mass for a rigid solid sphere is at the origin (0,0,0). I begin with the basic definition of CM ...
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1answer
25 views

Rate of change in size: Moving Objects

Is there a way of calculating the rate at which an object decreases/increases in size relative to the observer. For example, if a bus(4m wide) is moving away from a stationary observer at the rate of ...
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1answer
32 views

New direction vector after collision of spheres [closed]

I have a volume in 3-space in which random spheres are spawned in motion. They have the following attributes to them: position known (in three axes) a direction vector (in three axes) a scalar speed ...
2
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1answer
709 views

How small would the patch of sun be that delivers heat to the earth?

The sun, being a ball, projects its EM radiation and light in all directions. We earthlings only receive a light from a portion of the sun, not all of it. What size is this patch of the sun's surface ...
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0answers
50 views

Can quantum mechanics, general relativity and all physical theories be reduced to geometry? [duplicate]

I was told by my, perhaps ignorant (that is for you to decide), teacher that "all physical theories can be reduced to geometry in the manner of Newton's Principia/Euclid's Elements, however, due to ...
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1answer
61 views

Can 3 objects be collinear?

Suppose there are 3 objects floating in some space, without anything else besides this 3 objects. Is there any way for them to end up collinear at any given moment (assuming they start at completely ...
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3answers
100 views

Why sphere minimizes surface area for a given volume?

I was studying surface tension recently. Rain drops or bubbles of any kind which form are always of a spherical shape. This is because the liquid tries to minimize the surface area as the molecules ...
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0answers
198 views

The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
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7answers
5k views

Experimental evidence of a fourth spatial dimension?

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence ...
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0answers
26 views

How do quantum particles interact with each other? [closed]

Does infinite expansion of particles become finite when the smallest stuff that makes up matter interact with each other? Would then those particles be in the form of shapes,such as platonic solids ...
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3answers
2k views

How can we see the moon while it's between the Earth and the Sun?

I know this sounds like (and probably is) a stupid question, but I can't figure it out. As far as I know, the crescent shape of the moon is when the moon is on the sunny side of the Earth, but that ...
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0answers
20 views

Simple Stern-Gerlach Apparatus Orientation

I have been reading Townsend(2012)A Modern Approach to Quantum Mechanics. In the first chapter, he introduces the idea of intrinsic spin angular momentum, and some of its strange quantum properties ...
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3answers
4k views

Are circles stronger than triangles?

I've often herd in engineering that "there is no shape stronger than a triangle". I also recall that arches are very strong shapes as well, which can be crudely described as a ...
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1answer
46 views

Physics related derivation of equation of cycloid

So I was trying to find the path traversed by a point on the rim of a rolling disc. I eventually landed up at an equation but when I went to check it out in the internet, I couldn't find any similar ...
2
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2answers
154 views

Why is $\pi$ the value it is? [closed]

Why is the value of $\pi$ 3.141592...(etc.)? Is it a fundamental property of our universe? Or does it follow from our definition of what a circle is, or does it otherwise follow from the way we ...
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2answers
77 views

How to find the center of rotation? (2D)

First off, I'm assuming that a free floating polygon doesn't always rotate around its center of mass unless the net force is zero (based on the points below). If this isn't correct please tell me. ...
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1answer
82 views

What does the $a$ stand for in this picture? (And some clarification)

$$ I_{triangle} = \frac{b^3h-b^2ha+bha^2+bh^3}{36} $$ $$ I_{total} = \sum^n_{k=1}(I_{triangle}+Md^2)_k $$ Source is here. I'm trying to understand the mass moment of inertia in order to create a ...
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1answer
1k views

Land proportions in NASA blue marble photographs

What is the explanation for the apparent size difference of North America in these two photos from NASA? Image source Image source
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2answers
195 views

What is the difference between a hollow (sphere/cylinder) and a shell (cylinder/sphere)? [closed]

First of all, it was hard to "tag" this question ! Anyways, I see some contradictions in what a shell or a hollow cylinder is in some sources in the internet based on some figures they show. I ...