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

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1answer
212 views

Tensor of inertia

The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be ...
2
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2answers
126 views

Zwiebach quick calculation 2.5

I am working through Zwiebach's a first course in string theory. It's been a while since I did any math (or physics!), and I am stuck on the following problem (quick calculation 2.5 in the book): ...
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1answer
101 views

Making a cut trough a center of mass, can the masses of the pieces be equal?

Let's say point $P$ is the center of mass of an irregularly shaped object. If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same ...
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1answer
48 views

Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, ...
2
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1answer
129 views

Where is a closed form also exact?

I'm not very familiar with exterior derivatives. I've some trouble following argument (which is a part of a proof that if the Riemann tensor vanishes, $R^{\,\rho}_{\;\,\sigma \mu \nu}=0$, iff there ...
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1answer
165 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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1answer
76 views

virtual boxes mirror reflection

The problem statement Find the lightpath with a given starting and ending points via one or more mirrors. In those kind of problems you try image someone pointing a laser with a very narrow beam ...
4
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1answer
346 views

Problem in Youngs double slit experiment

This is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triangle have $90^0$ but what about others?
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1answer
88 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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1answer
1k views

Analytic solution for angle of minimum deviation?

Consider a simple prism with a prism angle $A$, angle of incidence $\theta_1$, angle of emergence $\theta_4$ and the first and second angle of refraction as $\theta_2,\theta_3$. the refractive index ...
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2answers
99 views

Density of a material in different dimensions

Hope this isn't something trivially wrong, I am a beginner in classical mechanics. But anyways, say there is a cube, of side length $a \ \text{cm}$. The volume of the cube is $a^3 \ \text{cm}^3$. If ...
7
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1answer
250 views

How did Eratosthenes know the suns rays are parallel?

Eratosthenes famously observed that the suns rays were perpendicular to the ground in one location, yet non-perpendicular to the ground at a location some miles to the north. On the assumption that ...
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1answer
331 views

Two formulas for a particle's acceleration

While on a class my teacher was taking about particle's motion in space. At some point she said the following: Consider that the particle's path is described by a curve in space defined by the ...
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2answers
94 views

Paralel light conditions after passing from a sphere

Is it possible to get such result that light will be parallel after passing from the sphere? what is the total condition for such result if possible? Thanks for answers
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2answers
112 views

Vectors question? [closed]

I am stuck on this vectors question I have for home work. Does anything think they can help point me in the right direction on how to solve this? An explorer is caught in a whiteout (in which the ...
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2answers
217 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
2
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1answer
148 views

Can two parallel lines meet? [closed]

My physics teacher talked about the meeting of 2 parallel lines, and he said that it may occur in the infinity or something. I know that 2 parallel lines can meet in spherical geometry, (thanks to ...
0
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1answer
56 views

Parametric equations of a hypersurface

In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations?
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1answer
410 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
1
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1answer
140 views

Characteristic length of a triangle [closed]

I am reading a paper on collision detection in cloth simulation, please help me understanding following lines written in the paper : To check if a point x4 is closer than some thickness h to a ...
2
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0answers
80 views

Geometry and physics [closed]

I'm searching for references, articles and books, that discussed the geometrization of modern (and contemporary) physics, in a philosofical point of view. Something in the way that Michael Friedman ...
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1answer
92 views

3D billiard with no gravity nor air drag

If I have a projectile shot in a vacuum-box that has no gravity or wind resistance inside it (lets say the box is 1000 units tall and 1000 units wide), with the only rule being that the projectile ...
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2answers
5k 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 ...
6
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2answers
854 views

Are there any naturally occurring perfect circles? [duplicate]

Given that $\pi$ is the irrational number that occurs with a perfect circle, and perfection is very difficult to achieve through chance or nature, I think that most circles are really ovals, and ...
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1answer
2k views

Minimum height of mirror required to view image

I wanted to know the minimum height of mirror required to be able to view a complete image of a person. I considered the following setup: $HF$ is the person in question. $H$ denotes the head, $F$ ...
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2answers
313 views

At what starting angle will a billiard ball hit a pocket? [closed]

Let's say you have a square pool table with one pocket. At what angles can you hit the ball to make it hit the pocket? What relation do these angles hare? Constraints: Table is square: $\ell=b$. ...
2
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2answers
179 views

Determine the effective radius of a gear?

I'm trying to determine the gear radius using a ruler by $cm$ but I just don't know what to measure: 1- the length from gear center point to the end of the gear tooth ? Or 2- the length from gear ...
2
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2answers
266 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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2answers
85 views

What is a geometrical object?

From the Wikipedia link for Geometry: Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position ...
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2answers
223 views

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

Among the other ways, one way to prove the Earth is round is the triple-right triangle. The idea is simple: Starting from point A you move in a straight line for a certain distance. At point B, ...
5
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2answers
308 views

Is length/distance a vector?

I have heard that area is a vector quantity in 3 dimensions, e.g. this Phys.SE post, what about the length/distance? Since area is the product of two lengths, does this mean that length is also a ...
5
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2answers
107 views

Which causal structures are absent from any “nice” patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?, where "causal separation structure" ($s$) should be ...
2
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1answer
124 views

Perfectly focusing refractive surface

On reading Feynman's lecture on physics, in the geometrical optics section he said that a curve which focuses all the rays coming from a point to another fixed point beyond the refracting surface ...
0
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1answer
38 views

Is there a term for the argument of the sine function outside of geometry?

Are there similar terms in other areas for the idea the "angle" conveys in geometry? I find that functions for abstract things such as pressure, electrical currents (nothing geometric there) on AC ...
8
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4answers
297 views

Physical representation of volume to surface area

I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume ...
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2answers
139 views

Limit on velocity in Minkowski Spacetime geometry

Let A be a rocket moving with velocity v. Then the slope of its worldline in a spacetime diagram is given by c/v. Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90. Does ...
3
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1answer
124 views

Uniqueness and existence of polygonal orbits through a spherical shell

Say we have a spherical wire mesh raised to a negative voltage. Then let's say we release a proton from near the surface, and away from the surface, at some angle and speed. Also, imagine that the ...
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2answers
104 views

Where to take $\theta$ (theta) in a triangle?

This is an inclined surface having and unit vector A. The perpendicular and horizontal surfaces are the components of the inclined surface. We want to find out that how much flux will pass through ...
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1answer
121 views

Rømer's determination of the speed of light

I am trying to understand Rømer's determination of the speed of light ($c$). The geometry of the situation is shown in the image below. The determination involves measuring apparent fluctuations in ...
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votes
2answers
790 views

How to determine Center of Gravity? [closed]

I came across this question while having conversation with one person. We know that Center of Gravity of a solid cube is at the intersection of connecting the opposite vertex of the cube. Suppose, you ...
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0answers
68 views

Geometry for Physics [duplicate]

I am currently a high school student interested in a research career in physics. I have self taught myself single variable calculus and elementary physics upto the level of IPHO . And I am comfortable ...
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0answers
29 views

Problem in geometrical optics [duplicate]

I was trying to solve a problem taken from an Physics Olympiad when I came across a curious and complex mathematical expression. I can not prove with what I know so far about mathematics, does could ...
1
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1answer
31 views

Asking about centrepetal acceleration

please look at the fig first 1) How can you claim that the triangle ABC is same as the triangle PQR? 2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB? ...
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2answers
372 views

Geometrical interpretation of complex eigenvectors in a system of differential equations

Let's consider a system of differential equations in the form $$\dot{X} = M X$$ in two dimensions ($X = (x(t), y(t))$). In the case that $M$ has real values, it is easy to give a geometric ...
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2answers
797 views

Calculate the center of mass of a semicircle [closed]

How I determine the center of mass of a semicircle using the definition of center of mass? I only know solve this using the Pappus theorem. Consider that the semicircle is centered on the origin and a ...
3
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2answers
163 views

Proof that a spherical lens is stigmatic

In geometric optics, we generally allow that, for example in the case of a convex lens, rays coming from a particular point get refracted towards another particular point on the opposite side of the ...
4
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1answer
430 views

How is the equation of motion on an ellipse derived?

I would like to show that a particle orbiting another will follow the trajectory \begin{equation} r = \frac{a(1-e^2)}{1 + e \cos(\theta)}. \end{equation} I would like to do this with minimal ...
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0answers
68 views

Water Stream from a Horizontal Surface

If water was projected from a flat surface where gravity was equal all over the surface. What would happen when the water fell in on itself? The water is in a continuous stream and is perfectly ...
3
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1answer
521 views

Nanotube chiral angle as a function of $n$ and $m$

I'm looking into nanotubes and I thought I'd assure myself that the basic geometry equations are indeed correct. No problems for the radius, I quickly found the known formula: $$R = ...
4
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1answer
125 views

How to assign coordinates to the elements of a flat metric space

Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements, and consider the assignment $c_f$ of coordinates to (the elements of) set $M$, $c_f ...