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

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0
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2answers
75 views

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

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 ...
0
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0answers
17 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
54 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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2answers
72 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
32 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 ...
2
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1answer
108 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
45 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?
-2
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1answer
77 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
32 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
55 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 ...
0
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1answer
35 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, ...
-2
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1answer
55 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
25 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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0answers
45 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
51 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 ...
3
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1answer
71 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
19 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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0answers
10 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
259 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 ...
2
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2answers
294 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
61 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 ...
0
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2answers
66 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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0answers
40 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 ...
1
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1answer
110 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 ...
1
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1answer
106 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 ...
0
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1answer
41 views

Moment of inertia tensor calculation [closed]

If I have a rigid body consists of three uniform rods, each of mass $m$ and length $2a$, held mutually perpendicular at their midpoints choose a coordinate system with the axes along the rod. So I ...
1
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1answer
47 views

Standardising shadow length on sundials

The sundial is fundamentally flawed in that the length of each hourly shadow changes with the seasons. If the base of the sundial was engineered to move cyclically on an anual basis however, the ...
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2answers
68 views

What should the length of my wire be in order to get a surface area of 10cm^2?

I would like to make a flat coil out of a steel wire that is $1.22 ~\text{mm}$ in thickness (or $1.22~\text{mm}$ in diameter). I wish to make the coil up the wire into a flat disk that has a surface ...
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3answers
40 views

Foci of elliptical path

I have read the Kepler's laws of motion where I came across the term foci of elliptical path. But what is really a focus? Can anyone please explain what is a focus (maybe with a diagram) and why a ...
3
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1answer
48 views

Why do you seem to go faster as you hug a turn?

I was driving to work this morning when this question occurred to me. I was going up a clover-leaf entrance ramp to the highway. The person in front of me was lazily floating the outside of the curve, ...
2
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0answers
49 views

Circumference measurement using a capacitive sensor

I have a question which I hope someone in here can help me answer. Background: I’m building a device where I intend to use a stretchable capacitive sensor to define the radius change of an object. ...
0
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2answers
70 views

How to calculate centre of mass

How do I find the centre of mass with given coordinates? For example if we have four objects with mass $m$ at coordinates of a square $(0,0,0),(0,0,a),(0,a,0),(0,a,a)$ or another example with eight ...
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0answers
20 views

Constructing uniform mesh in reciprocal space?

This is a bit of a mental exercise for me to get comfortable with the math of reciprocal spaces since I am going to start doing some research that requires knowledge of reciprocal spaces. Let's say I ...
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1answer
113 views

How to derive path difference ($\Delta l=d\sin \theta$) for double-slit interference?

The Wikipedia page for the double-slit wave interference experiment states that the path difference between waves diffracting from the two slits is equal to: $$ \Delta l=d\sin \theta $$ where $d$ is ...
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3answers
933 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 ...
1
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0answers
178 views

Can the universe be round but still infinite?

Can the universe still be infinite in space if its curvature is > 1? Is a manifold of positive curvature necessarily compact? Does the Tarski paradox have any bearing on the finite or infinite ...
3
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1answer
298 views

Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
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0answers
29 views

Radian Zeno-version paradox: Can a particle moving in the circular path reach the angular position of non-terminating decimal form radian value?

Consider a particle P moving in a circle of radius r as shown in the figure. Premise 1: Position of the particle can be described by the angle $\theta$. Premise 2: Particle reaches the position ...
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1answer
151 views

Constrained Motion of Connected Particles, Small Calculation Question

I am looking at this sample problem from Meriam Kraige - Engineering Mechanics Dynamics: When I do the differentiation, I end up with $\large -2\dot y+\frac{x}{\sqrt{x^2+h^2}}$ Where is the $\dot ...
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1answer
386 views

Center of mass of equilateral triangle

I'm trying find the center of mass ($R$) of a uniform density equilateral triangle without using symmetries to find the x coordinate of the vector $R$, but I can't get the expected $R_x = ...
1
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1answer
76 views

Calculating the area of region of the sky

I am given the right ascensions ($\alpha_1$ and $\alpha_2$) and declinations ($\delta_1$ and $\delta_2$) of a specific region of the sky. How can we find the area of this region? I know that there ...
11
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3answers
1k views

How many times can light revolve around a black hole?

Take a light ray approaching a black hole from infinity which goes out again to infinity. What is the maximum finite rotation it can describe? (I know it can loop around indefinitely in the ...
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0answers
59 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
18
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4answers
3k views

Distinguishing between solid spheres and hollow spheres (equal mass)

If there are two spheres (hollow and solid) with equal mass and radius and we want to find the hollow sphere without using any equipment. What's the best way(s) to recognize the hollow sphere and ...
0
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1answer
46 views

Quantum physics and constructable numbers [duplicate]

I do not know much about quantum physics. However, I do know it believes the world is discrete ( has quanta). This seems to contradicts the fact that we can create an object of length root 2 since you ...
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0answers
27 views

Is the total length of the inner sheet of a two ply roll of toilet paper shorter than the outer sheet?

If you look at any individual square of two plies, each ply looks the same. But musn't the inner ply be shorter? Wouldn't the inner ply develop kinks if it was the same length as the outer ply? Or ...
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1answer
37 views

Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
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0answers
43 views

Why is space 3 dimensional and could it be different? [duplicate]

Is there any particular physical law or property which caused space to be 3 dimensional, and is there theoretical possibility of having more or less dimensions in physical space?
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2answers
168 views

What is the connection between geometry of physical space and Hilbert space?

In Quantum Mechanis (QM), the dynamical variables are the (quantized) coordinates $x_j$ and their canonical conjugate $p_j = -i\partial_j$ with the commutation relation $[x_j,p_k]=i\delta_{jk}$ ...
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0answers
46 views

What's wrong with this calculation of the center of mass of a triangle?

Find the center of mass $(x_G,y_G)$ of a homogeneous triangle of mass $m$. Divide it into infinitesimal rectangles of width $dy$, length $x$, mass $dm$ and area $dA$. We have $d A = x dy $ ...