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

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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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0answers
28 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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36 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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1answer
60 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 ...
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211 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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0answers
149 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? ...
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2answers
158 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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3answers
118 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
96 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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2answers
537 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 ...
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41 views

Given a dimension of a known object in the image, how can we calculate the dimension of other objects in the same image ?

The question considers a very specific scenario in which we have an image with let us say, two rectangle objects. We know width and height of one object. How can we calculate the dimensions of the ...
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1answer
61 views

A teaser on center of mass of right circular cone?

How can a distinction be made between the centre of mass of a right circular cone As a uniform solid ($\frac{h}{4}$ from base, where is $h$ is height) and That composed of infinitesimally small ...
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3answers
83 views

Absolute direction in space [closed]

Rotation, from my understanding, is basically the "exchanging of different spatial dimensions with eachother", with $x^2+y^2=d^2$ being the "relationship" between any two spatial dimensions, aka. if ...
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4answers
243 views

Is there a geometric interpretation of the spacetime interval?

In Euclidean space, the invariant $s^2 = x^2+ y^2+ z^2$ is equal to the length square of the position vector $r$. This is easily understood and can be represented geometrically in a graph. On the ...
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1answer
405 views

Center of mass (COM) of a uniform quarter disk [closed]

I was trying to calculate the coordinates of the COM for a uniform quarter disk. By symmetry, it must lie on the angular bisector of the central angle. Also, $A=\frac{\pi R^2}{4}$, thus ...
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3answers
201 views

What is the meaning of “a straight line”? [duplicate]

The book "The Dancing Wu Li Masters" page 189 talking about General Relativity says "A geodesic is not always a straight line". Is that true? What is a definition of "straight line" that makes sense ...
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1answer
29 views

Investigating volume of a crater

I determined the shape of the crater to be a spherical cap. According to this website, http://mathforum.org/library/drmath/view/55253.html , its formula is described as $$V_{cap} = \frac{1}{6} \pi h ...
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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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7answers
3k views

How big are clouds? [closed]

How big are clouds? When I look up into the sky I have no frame of reference, so I don't know if they are 200 feet or 2 miles across. When I am in a plane looking out at a cloud, I try to use the wing ...
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2answers
392 views

How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
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1answer
59 views

Order of magnitude for the range of vision

Let's say you're in the middle of a desert, with nothing but sand. Let's also assume that you have a 20/20 vision. When you're just looking there's a point that your eye can't reach name it $M$ and ...
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1answer
400 views

Centre of gravity vs centre of mass for a pyramid mounted on a cube, all sides of length $l$ [duplicate]

A uniform solid body is constructed using a square-based pyramid mounted on a cube. If each edge of the solid has length $l$ show that the centre of gravity of the body lies within the cube is, $\frac ...
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2answers
150 views

Why does a circle and square of same length occupy different areas? [closed]

May be this question do not meet the standards of this blog but i was just calculating on things and i got stuck..actualy we were playing this game in which we were to fill students in a square and ...
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0answers
34 views

Will a string always be tangent to a pulley at 45 degrees above the horizontal?

I just spent about an hour trying to figure out which part of my calculation was giving me the incorrect answer, and now I've finally got it. At first, it made sense,but now it doesn't again. There ...
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2answers
348 views

Why railroad tracks seem to converge?

I stand up and I look at two parallel railroad tracks. I find that converge away from me. Why? Can someone explain me why parallel lines seem to converge, please?
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137 views

Very basic question about vector

The vectors $a = (2,-1,-2)$ and $b = (0,-3,4)$ are given. Determine $a$:s parallel and normal vector to $b$. Obviously the parallel vector should be the dot product $a \cdot b$ times the unit vector ...
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0answers
41 views

What is the scale factor of a hyperbolic universe?

I wanted to derive the solution to this question from the Friedmann equations myself but I ran into some trouble. I was working in natural units where $c=G=1$, then, for brevity, I defined ...
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1answer
29 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
129 views

Why Newton wanted lines to be generated by continued motion of points rather than by apposition of parts?

The following passage has been extracted from the Newton's (John Stewart's English translated version) "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an ...
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1answer
235 views

Derivation of vector cross product [duplicate]

Everyone of us know about the vector cross product. But I wonder, how the formula of $AB\sin\theta$ has been derived? Can anyone help?
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1answer
114 views

Where is error in this method of finding volume of sphere using integration? [closed]

Where is error in this method of finding volume of sphere using integration?
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1answer
46 views

Eulerian angle understanding

I have alot of confusion with Eulerian angle so first of all I would like to address something I don't understand from the book and maybe that would shed some light on the intuition of eulerian ...
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2answers
155 views

If planet orbits are in the shape of an ellipse and the sun is a focus, where and what is the focus? [duplicate]

I've studied ellipses. I've studied physics. But when it comes down to the elliptical orbits of the planets is where I get confused. Ellipses contain two foci — and in the orbits of our solar system ...
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1answer
49 views

Model of spherical wave fronts in relativity

In relativity, the 3-surface formed by light rays emanating from an event as they evolve in time has the shape of a hypercone wich is flat. I have difficulties seeing how can a spherical wave front, ...
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1answer
64 views

Why are these two angles the same? [closed]

I can't find no similar or other relations between the two triangles, the two right triangles. However, if I look at it this way, the two triangles are indeed similar. But then this is a whole ...
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1answer
29 views

Waves interfere in angle equation

If we had two waves perpendicular to each other, with equations: $x=α \sin(ωt)$ (1) $y=β \sin(ωt+π/2) ==> y=β \cos(ωt)$(2) $\sin(ωt)^2+\cos(ωt)^2=x^2/α^2+y^2/β^2=1$ $x^2/α^2+y^2/β^2=1$ is an ...
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90 views

Are Landau levels always degenerate?

Solving the Landau problem, namely the quantum mechanical problem of a particle in a magnetic field leads to degenerate energy states, the famous Landau levels. My question consists of two parts. ...
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0answers
54 views

Compute distance travelled based on a yaw-rate

Assume that a rigid body is traveling with constant velocity $v$, and (this rigid body) is rotating with a constant yaw rate of $\dot{\theta}$. Find the distance travelled in one time step, $\Delta ...
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1answer
107 views

Does charge bend spacetime like mass? [duplicate]

Does charge bend spacetime like mass? I'm not asking if electromagnetic forces can be described geometrically, but if EM fields could correspond to particular curvatures of spacetime, like gravity ...
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0answers
31 views

Get actual object size in mm using camera [closed]

How to get actual object size in mm when we know Object distance, focal length, image width in pixels and camera angle,
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1answer
47 views

Coulomb collision

I was reading an article by N. Bohr and came upon the following problem (the following wording is actually taken from a book by Thompson - Conduction of Electricity Through Gases): Let $M_1, M_2$ ...
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0answers
21 views

How is the inertia tensor (just diagonal elements) of a quarter disk related to the full disk one?

Let be a disk of radius $R$ and mass $M$ with an uniform distribution of mass $\sigma$, centered in the origin O, laying in the $OXY$ plane. If I know that $$I_x=I_y=\frac{1}{4}MR^2, \qquad ...
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4answers
396 views

Why perpendicular vectors do not share components?

I just can picture it in my mind or on paper. Can someone explain it with examples? This is the key idea behind the uniform circular motion: if the force has a component in direction of the object's ...
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2answers
396 views

Sound source not in a straight line with the sound receiver - does that make a difference?

Hope the graphics will help me explaining my question better. Let's say the box would be a room in the fourth floor, and the sound source would come from cars in the street. It is clear that in ...
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1answer
77 views

Why is the elemental volume of a sphere equal to $4 \pi r^2dr$?

I was doing this question on calculating the electric field at a certain point in a sphere (length $r$ away from the centre), where the charge density is given by an equation. When I checked the ...
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2answers
99 views

Physical Meaning of Cone used in Conic Section for Orbital Mechanics

Does the polar angle (complement of $\theta$ below) of a cone which intersects a plane to yield a conic section have a physical meaning in orbital mechanics? Note that the angle of incident ...
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55 views

Alternative ways of calculating the principal moment of inertia

Let's say I am given 2x2 masses ($m$ and $m'$ have the same mass, just different coordinates): $m_1: (-a,b,0)$ $m_1':(a,-b,0)$ $m_2: (a,b,0)$ $m_2': (-a,-b,0)$ Due to symmetry the center of mass ...
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1answer
192 views

How fast would one have to travel in an airplane in order to experience a continuous sunset?

For the sake of simplifying this problem and removing any guess work on how high the plane is flying, we'll say that our airplane is at 30,000 ft. as this is the average altitude for commercial ...
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1answer
151 views

Trajectory of a swimmer trying to reach the opposite bank [closed]

I came across the following question 2 days ago: $Q$. A swimmer is swimming in a river with a speed $u$ with respect to the speed of water which is $v$. It is assumed that the river has straight ...