Curvature Definition and 872 Threads

A train is moving towards north at one place. it turns towards north east. here we observe that the radius of curvature of outer rail will be greater than that of inner rail why?pls explain velocity and radial acc. are the same and radius of curvature=v^2/a normal

Seen a couple of pieces on gauge theories of finance equating arbitrage opportunities to curvature, for this to work the curvature must therefore not be constant, instead it would be some sort of a function of capital flows

How to prove the radius of curvature at any point on a line? In a magnetic field, field lines are curves to which the magnetic induction B is everywhere tangetial. By evaluating dB/ds where s is the distance measured along a field line, prove that the radius of curvature at any point on a...

In a magnetic field, field lines are curves to which the magnetic induction B is everywhere tangetial. By evaluating dB/ds where s is the distance measured along a field line, prove that the radius of curvature at any point on a line is given by density symbol-->p= B^3 / [ B x( B * del) B]...

I have seen in a few places around the web that the margin of error for the flatness of the universe is about 2%, but haven't seen any citations. Could anyone refer me to a reputable paper that I could cite that mentions what this margin of error is? Thanks!

Obviously not. But I am confused on this. Newtons laws of gravity did not fit with Einsteins Relativity theories because Newton said that a change in matter of an object would cause a shift to be felt by others in the universe because of the change in gravity. This would mean that the movement/...

Simple question (I think). According to GR, is gravity no longer thought of as a force of attraction, but simply a curvature of space-time induced by mass? The earth, for example, creates some kind of "space-time well" that keeps us in our seats as we type on our keypads? (That's poorly...

Hello, I have what is probably a relatively (no pun intended) simple question pertaining to general relativity. I thought that I had achieved a solid understanding of the theory (and its special counterpart), until this question formed in my mind. My problem is based on the following...

I understand that Gravity is the result of spacetime curvature. All planets are spherical(almost). Planets are spherical because of gravity (partially true at least). So, seriously, what came first? If we have just mass of gas - how would it become spherical -if gravity were only because of the...

Homework Statement Let \underline{r} be a regular parameterisation of a space curve C \subset R^{3}. Prove that \kappa=\frac{\left\|\underline{\dot{r}}\times\underline{\ddot{r}}\right\|}{\left\|\underline{\dot{r}}\right\|^{3}} . The Attempt at a Solution We have...

How has the curvature of the universe changed with time? I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what \Omegak could have been like before...

I have an equation for a curve that lies along the surface of a truncated cone. In polar coordinates: theta(r) = K * [ U + arctan(1/U) - (Pi/2) ] where: U = SQRT[ ((r/r1)^2) - 1 ] K = SQRT[ 1 + (H/(r2-r1))^2 ] r = r1 + (r2-r1)(z/H) r1 = minor radius of the truncated cone r2 =...

Study the curvature and the asimptotes of the function x+\frac{lnx}{x}.

If I dig 2 holes a little space apart, and then they intersect straight down, because of the curvature of the earth, then there is more than one up direction from the center. The closer 2 points at an equal distance down from the surface in separate holes get to the center, the less distance...

Schwarzschild example: Two observers orbit around the same central point mass at different radii. They measure that the radial separation between them is greater than their orbital circumference / 2pi. They conclude that there is negative (parabolic) spatial curvature in the radial direction...

Hey all, Thought I'd post this here as it is a little tricky trying to get a straight answer from the boys and girls of theory over at the GR/SR section without causing havoc of some kind. It seems to be fairly well accepted that space-time is curved. So maybe someone here can answer the...

I've read in a few places that the energy and momentum of the electromagnetic field will itself induce a curvature of spacetime, much like the presence of matter. I'm not very familiar with general relativity, but does this imply that particles with mass and zero charge will still be affected...

I've been wondering if there is a relationship between the mass of an object and how much it "curves" space-time. I can't seem to find an equation or connection, I have looked at four-momentum but am not certain what it actually calculates. Maybe I just don't know it and there is yet an equation...

discuss how to find the umbilic points of an ellipsoid and their connection to lines of curvature.

who can help me with this: on an ellipsoid most points are not umbilic, but there are some special places that are. Discuss how to find these points and their connection to lines of curvature.

Homework Statement Suppose that I want to compare the Kinetic Energy of an electron to the Kinetic Energy of an alpha particle if they both have the same radius of curvature in a magnetic field. Homework Equations qvB = mv^2/r KE = 1/2 mv^2 The Attempt at a Solution I am...

Homework Statement An object is placed 15cm from a certain mirror, the image is half the size of the object, upright, and virtual. how far is the image fromt he mirror, and what is the radius of curavature of the mirror? Homework Equations 1/f = 1/p + 1/q f= r/2 The Attempt at a...

When it comes to emulsions and microemulsions; what does oil/water curvature mean? What does it mean that microemulsions have high oil/water curvatures, while emulsions have small oil/water curvatures?

I really need help answering these questions: use the gauss map to find the gaussian curvature of a sphere of radius r at any point. also, use the gauss map to find the gassian curvature of a cylinder of radius r at any point.

The Einstein field equations (EFE) in 4 dimensions have 10 degrees of freedom; The Riemannian curvature tensor in 4 dimensions has 20. If I understood this correctly, one can split up the curvature tensor and describe the remaining degrees of freedom by its traceless part, which is called the...

Homework Statement Derive an expression geometrically for the radius of curvature of the following beam. This is part of a lab assignment for the bending of a simply supported beam with overhangs. ** I did this crappy diagram with AutoCAD, so I couldn't ( or didn't know how to ) include...

http://www.mth.uct.ac.za/omei/gr/chap6/frame6.html" is a derivation of the components of the riemann curvature tensor. the problem is that i can't understand the transition between eq97 and eq89 . what does "To lowest order " mean ?

Why is the definition of the curvature form for a Cartan connection the correct definition, and what does it actually tell you? I've read that it "measures the failure of the structural equation" but I suppose I don't really understand the structural equation (of a Maurer-Cartan form) anyway...

A doubly charged helium atom (mass = 6.68 x 10-27 kg) is accelerated through a potential difference of 4.00x 103 V. What will be the radius of curvature of the path of the atom if it is in a uniform 0.450 T magnetic field? the equation i was using was r = mV/|q|B m = 6.68 x 10^-27 V =...

Hello, I have a question related to the calculation of curvature using exterior differential forms (Misner, pp. 354-363). In all the examples given in the book (i.e. Friedmann, Schwarzschild, pulsating star metrics), the "guess and check" method used to find the connection forms (Eq. (14.31))...

A production line inspector wants a mirror that produces an upright image within magnification of 7.9 when it is located 10.0 mm from a machine part. What is its radius of curvature? I used: r/2 = f 1/f=(1/do) + or - (1/di) m=di/do first i did 7.9=10/do then i found that...

Homework Statement Use the same device to separate singly charged CO2 having 12C and 14C. What are the radii of curvature? This is a follow up question based on a HW problem I answered last week. The original problem was this: A doubly charged helium atom is accelerated by a voltage 2700V...

Homework Statement I am given a space curve r(t)= t i + sin(t) j and point (pi/2,1). They ask me to find an equation for the circle of curvature. Homework Equations Kappa, T, N, not sure The Attempt at a Solution So I have found the radius of curvature which is row= 1/kappa=...

Homework Statement Find the curvature of x = e^(t) y = e^(-t) z = t t = 0 Homework Equations I've used the equation of k(t) = |r'(t) x r''(t) |/ |r'(t)|^3 The Attempt at a Solution k(t) = |r'(t) x r''(t) |/ |r'(t)|^3 = |e^t i + -e^(-t)j + 1k| x |e^t i + e^(-t)j +...

My teacher wrote an alternative equation on the board for curvature, and I am wondering how it is true: k = | dT/dt / |dR/dt| | where T is the unit tangent vector. I know k = |R' x R''| / |R'|^3 = |dT/ds| but I am not sure about the formula in question. How is it true/derived?

I have searche many general relativity texts and have not found an answer to the following question: How does curvature translate into the Newtonian idea of gravitation? For example, how is Newton's law of gravitation, where all matter attracts all matter, an approximation to the idea of...

Does the curvature of spacetime describe gravity or tidal force?

This is a problem I'm having reading Visual Complex Analysis, page 295. If you look up "pseudosphere circles of curvature" on Google, it should be the first thing listed. On a point of a psuedosphere, there are 2 "circles of curvature", one with its center on the normal pointing out and the...

Homework Statement Show that this statement is false: when a moving particle along a curve reaches its max. speed at t=3, its acceleration is 0. Homework Equations a = d^2 R / dt^2 = d|v|/dt * T + k |v|^2 N where k = |dT/ds|, T = v/|v|, N = 1/k dT/ds The Attempt at a Solution...

Homework Statement A doubly ionized atom (charge = +2e) whose mass is 5.15E-26 kg is accelerated by a voltage of 3450 V and enters a region where a uniform magnetic field B = 0.100 T acts perpendicular to its motion. What is the radius of curvature of the path of the ion in the B-field...

Please note that I do NOT want to discuss whether gravity is a force or the effect of space-time curvature here. If you want to discuss this, please post a separate topic about it. What I wanted to ask is what Einstein's own beliefs on this were. Up till now I had always believed he had...

Homework Statement A surface is formed by revolving y=x^(8/5) / 4 between [0,5] about the y-axis. Find the curvature of the generating curve. Graph the function of the generating curve. This is a question from a mathematica project. The book we are using is Stewart Multivariable Calculus...

According to wiki under http://en.wikipedia.org/wiki/Kretschmann_scalar" - While Riemann curvature tensor is proportional to tidal forces (\Delta g=2Gm/r^3), in some models of rotating (and charged) black holes, K is considered to diverge at the Cauchy horizon while tidal forces remain finite-...

Homework Statement Hi, I'm wondering if this is the proper way to approach this problem. The question says to: a)find the electric field at the center of curvature of the hemisphere (center of the flat bottom). Homework Equations Gauss's law: integral E*da = Qencl/epsilon...

Hello all. I understand that a two dimensional surface can have curvature without it being referred to a higher dimension. So that a surface such as that of a sphere does not need to refer to a third dimension to determine its own intrinsic curvature and so on for higher dimensions. Can a...

I think about general relativity often, specifically about the curvature of spacetime in the presence of matter (gravity). For a while, I understood much of this concept, but certain things escaped me: when objects are moving, it is easy to see how curved space causes matter to move in the way...

Hi there In an experiment I have calculated the radius of curvature for a +0.25D lens using Newtons rings and have obtained a value for 892mm, but the radius of curvature for a +0.25D lens is just over 2 metres. why is the value i got so much lower? do i have to double the value i got for the...

First I thought If nothing can move faster than c, then nothing can accelerate faster than c/sec, right? Well, that means that the maximum amount space-time can curve is up to the ol' 45 degree slope, not like straight down as some black-hole pictures are made. Right? And then I thought...

Homework Statement I'm trying to find a surface of revolution with Gauss curvature K of +1 at all points, which doesn't lie in a sphere. Homework Equations The surface is parametrized as \psi (t, \theta ) = ( x(t), y(t) cos \theta , y(t) sin \theta ) I have the equation K =...

Homework Statement If c is given in terms of some other parameter t and c'(t) is never zero, show that k = ||c'(t) x c"(t)||/||c'(t)||3 The first two parts of this problem involved a path parametrized by arc length, but this part says nothing about that, so I assume that this path is not...