Questions tagged [geometry]

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

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27 views

Center of mass of hemisphere

While calculating the center of mass for hemisphere, In solid hemisphere, we can calculate without taking the trignometric limit, Elements can be taken in terms of $y$ (vertical axis) and I got the ...
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25 views

For the vector in the $yz$ plane lying halfway between the $y$ and $z$ axes, how to find $\phi$? [closed]

I am solving a problem in spherical coordinates , there we have condition that a vector in the $yz$ plane lying halfway between the $y$ and $z$ axes. For this we take $\theta = \pi/4$ and $\phi= \pi/2$...
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31 views

Sign of components of $\vec{L}$ seems to change under parity; book says otherwise

Book: Gravitational Waves-Vol 1 by Maggiore; pg 147, note 48 The book says that the components of angular momentum $\vec{L}$ are unchanged under parity (reversing the orientation of the axes). Now, ...
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2answers
51 views

How to find resultant vector's angle? [closed]

Hi there, I am confused about why the vector diagram in the answers for the question above is drawn as such. I thought it would be drawn like this: My vector diagram gives a resultant vector which ...
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2answers
44 views

Finding the distance travelled by a fly in a room from one lower corner to the diagonally opposite one [closed]

A room has a length of 4 meters, width of 5 meters and height of 3 meters. A fly is on one of the corners and walks to the diagonally opposite one. What is the length of the shortest possible ...
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3answers
50 views

Why do mirrors reflect light while regular surfaces don't?

i understand about reflection and how we see light but what confuses me is; all objects that can be seen reflect light (besides black obviously) and mirrors also reflect light. so why does one produce ...
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1answer
43 views

Would it take more, or less than twice the force to inflate a balloon to a radius twice as big? [duplicate]

I'm making a set of exercises as part of a college project, aimed at 4th year middle school physics. In an exercise on spring constants, i used balloon inflation as a new example, i made the following ...
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29 views

Parameterizing an $n$-sphere [migrated]

Consider an $n$-sphere embedded in $n+1$ Euclidean space. What is the parameterization of that surface expressed as a Euclidean vector $\{x_1,x_2...x_n\}$. It seems like it should be $x_1=\sin\...
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2answers
146 views

Equivalent representations of path difference? (Laue equations and Bragg's law)

My textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou, presents the following image and explanation in a section on x-ray diffraction and Laue ...
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2answers
37 views

Change in areal element

I am reading Griffith's Introduction to Electrodynamics., On example 1.7 while calculating surface integral of $x = 2$ for a cube of side 2., the book states $da = dy \cdot dz$ I don't get this, what ...
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584 views

Determine Earth's radius with stopwatch at sunset [closed]

This question appeared on Bangladesh physics Olympiad 2014, Sylhet, Bangladesh for students of class 9 and 10. I really tried to solve this, but I failed. Please help. Suppose that, while lying on ...
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1answer
33 views

On earth, is a levelled ground perpendicular to the radius of earth?

During construction of a building we level the ground using laser or more simply a water pipe. Method using water pipe: We level the ground such that the water level is same at all four corners ...
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2answers
200 views

Dot products in spherical polars?

In the book classical mechanics, it said that since the three unit vectors $\hat r$, $\hat \theta$ and $\hat \phi$ are mutually prependicular, we can evaluate dot products in spherical polars in just ...
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1answer
32 views

About an angle approximation used in Feynman's treatment of Fermat's principle

In this lecture about Fermat's principle, Feynman derives the refraction law using the principle of least action. He finds the shortest path between $A$ and $B$ by defining a variable point $X$ and ...
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1answer
43 views

In two-dimensional polar coordinates,why does below approximate valid?

$$\Delta \hat r\approx \Delta \phi \hat \phi$$ where $\hat r$ and $\hat \phi$ is the vector unit in two-dimensional polar coordinates. I can't understand it when I am learning the Classical ...
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1answer
16 views

Orbital distances of planets [duplicate]

So is the exponential pattern in the planetary distances related to Johann Kepler's discovery in 1596 that the ratios of the orbits of the six planets known in his day were the same as the ratios ...
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3answers
83 views

How a wedge is two inclined planes?

All sources say a wedge is simply two inclined planes. I see how this is true geometrically, but I don't get how this is true functionally. In an inclined plane, the amount of force required to be ...
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1answer
104 views

Probabilistic stacking of blocks [closed]

This is a variation on the stacking problem. A block is a 1D object of length L and uniformly distributed mass. (with some negligible thickness). A stack of size n is a series of n blocks placed flat ...
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8answers
8k views

Why do we use cross products in physics?

We can define cross products mathematically like if we take two vectors, we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical ...
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3answers
77 views

Projection of elliptical motion

SETUP :- Here I have a line that rotates with a constant angular velocity and intersects a circle and an ellipse. The ellipse's major axis is equal in length to the diameter of the circle. The ...
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1answer
24 views

How does the distance in reciprocal lattice relate to distance in real lattice?

Suppose a two-slap of silicon is the distance 'a' apart in real space. What is distance between them in reciprocal space.
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2answers
102 views

Is the defintion of *inertial reference frame* given by Blandford and Thorne acceptable?

Edit to add: A simple explanation of my objection to Blandford and Thorne's definition of inertial reference frame (which they use synonymously with inertial frame) is that, if I'm in free float, ...
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1answer
52 views

Geometrical optics problem and broader questions about the correct use of $\approx$ in physical calculations

My textbook, Fundamentals of Photonics, Third Edition, by Saleh and Teich, gives the following: This seems to be mathematically incorrect to me? Firstly, the author stated that $\phi = \psi - \...
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1answer
128 views

What is the length of the yarn in a ball of yarn? [closed]

The image https://commons.wikimedia.org/wiki/File:Ball_of_yarn_10.jpg shows a typical ball of yarn. Such a spherical ball of radius $R$ has a volume $4πR^3/3$. The radius of the yarn is $r$. How long ...
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8 views

Calculate the changing morphology of a rubber ball

Imagine you have a rubber "bouncy ball" and you push your thumb hard into the ball. Some deformation will occur around your finger. However, the general morphology of the ball won't change in the same ...
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31 views

What is meant by “neighboring points”?

I have recently been frequently encountering the phrase "neighboring points" during my studies. For example: Fermat's Principle. Optical rays travelling between two points, $A$ and $B$, follow a ...
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3answers
101 views

If extra dimensions are out there, why don't/can't we see them? [duplicate]

String theory proposes the existence of extra space dimensions. Very brilliant minds believe in their existence. Of course, I could appreciate that they are consequences of mathematical ...
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3answers
445 views

Can we see the curvature of a surface?

After reading the Feynman lectures' (chapter 42, Vol.2) , it had me thinking if it is by any way possible to measure the curvature of a surface (think, surface of earth) just by observing the nature ...
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1answer
149 views

How many images are formed when an object is placed between two plane mirrors with angle $72^\circ$?

I'm a little confused here since there are varying answers on the internet, and I cannot find any legitimate sources explaining this problem. According to what I've seen, the formula is simply $$ N = ...
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1answer
263 views

What are the points in spherical coordinates?

Let's use the spherical coordinates so that $\vec P=(r, \theta, \phi)$. In this context i've read that it's possible to write $$\vec P'=\vec P + d\theta\ \vec e_\theta+d\phi\ \vec e_\phi+dr\ \vec e_r$$...
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2answers
120 views

With north and south poles fixed, do all geodesics have constant $\theta$ and $\phi$?

I was going thorough reading Kolb and Turner's The Early Universe where in Section 2.2 it starts by asking the following question. For a comoving observer with coordinates $(r_0,\theta_0,\phi_0)$, ...
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3answers
66 views

Does temperature coefficient of resistance depend on geometry?

By temperature coefficient of resistance of a material about a reference point $T_0$, I mean $${1\over R(T_0)} \left.{dR\over dT}\right|_{T_0}.$$ All the sources (that I’ve seen) that quote this ...
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1answer
56 views

What's the meaning of the coordinates if we use a polar coordinate system?

In general, the coordinates of a vector are defined as the projections of it onto the coordinate axis. Moreover, in a polar coordinate system, the basis vectors $\hat e_\phi$, $\hat e_r$ depend on the ...
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4answers
116 views

3 Dimensional Law of Cosines? Magnetic Vector Potential Problem

I am working on a problem similar to one in my textbook - however, I am having an issue understanding the example. Can someone explain the formulas from this picture? I am confused about using the law ...
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1answer
42 views

Intuitive understanding of angular momentum in cartesian coordinates

If a point-mass body is moving in a plane $z=0$, its angular momentum can be taken to be a scalar, and from the vector product formulas (assuming $m=1$ as I'm only interested in geometry), its value ...
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11answers
8k views

Is the “spacetime” the same thing as the mathematical 4th dimension?

Is the "spacetime" the same thing as the mathematical 4th dimension? We often say that time is the fourth dimension, but I am wondering if it's means that time is like the fourth geometrical axis, or ...
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2answers
59 views

Are there two ways of representing a vector i.e., parrallelogram and resolution?

the question was: The component of a vector is (a) Always less than its magnitude (b) Always greater than its magnitude (c) Always equal to its magnitude (d) None of these ...
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1answer
110 views

Why does a wormhole have this metric?

I asked this (or something similar) within another question and was asked to post it separately, so here goes: The metric for flat Minkowski space is: $$ds^2 = -dt^2 +dr^2 +r^2(d\theta^2+d\phi^2\sin^...
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1answer
66 views

What's the problem with Euclidean geometry for astronomical phenomena?

This passage from John Pierce, An Introduction to Information Theory: "also note that while Euclidean geometry is a mathematical theory which serves surveyors and navigators admirably in their ...
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1answer
96 views

Weird assumption in a paper to prove equation [closed]

Let $M_k$ and $M_{k+1}$ be two successive positions. Supposing the road is perfectly planar and horizontal, as the motion is locally circular, we have: Where $\Delta$ is the length of the circular ...
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0answers
32 views

Is every observer equidistant in all directions from the point of origin of the universe? [duplicate]

I am interested in the origin and present structures of the dimensions of space and time. I do not think space/time can be correctly described by an ordered set of scalars: (x,y,z,t). So. If every ...
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0answers
33 views

Square gears pitch curve relationships [closed]

I am trying to design square gearset using MATLAB program. I have designed several ones (elliptical, eccentric, spiral, circular ....etc). But when I came to the square gears, I needed the ...
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1answer
52 views

Are special conformal transformations continuous?

My understanding of special conformal transformations (SCTs) is fairly limited, but I believe that they are composed of an inversion, a translation and another inversion. Since inversions are discrete ...
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1answer
70 views

Why do the rail tracks seem to converge and vanish? [duplicate]

Why do railway tracks seem to converge at a far away point? Can this phenomenon occur with a very far away tall wall (considering I stand on a flat plane, not the curved surface of earth). Isn't ...
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1answer
111 views

How did German radio beams reach distant English cities during WWII? [closed]

During WWII, the Germans were using radio beacons (the "Knickebein" system) to guide their bombers into English territory. They set up two beacons, one in Kleve, a city in West Germany, and one at ...
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1answer
34 views

How can we find the charge distribution of $n$ external electrons on the surface of a conducting cube? [closed]

Suppose we take 'n' electrons and put them on the surface of a conducting cube. How can we calculate the charge distrubution and position of these electrons once the static situation has been arrived ...
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0answers
28 views

General force between two point particles, one of which has “spin”

Consider two points in the empty (isotropic and homogeneous) space: since the only vector that "makes sense" (the only vector that we can define) is the vector given by the difference of the two ...
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2answers
197 views

How to determine the minimum force in these questions?

Take a look at this example The author mentioned that the shortest path when the angle is 90 which is clearly obvious. Now take a look at the following problem from the same book The author has ...
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2answers
193 views

Confusion about a claim in the “Brief History of Time” by Hawking

In the first chapter, while talking about how Aristotle was able to conclude that the Earth is spherical, Hawking says that had the Earth been a flat disk the shadow of the on the Earth on the moon ...
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2answers
104 views

If vector $a$ rotate about vector $b$, does vector $b$ also rotate about vector $a$?

For $2$ vectors $\, \vec a,\vec b$, both originate at $[0,0,0]$: If vector $\vec a$ rotates about vector $\vec b$ when observed from a coordinate system fixed to vector $\vec b$, does vector $\vec b$ ...

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