Curvature Definition and 872 Threads

:confused: Can anyone explain what i am doing wrong? I thought the radius of curvature is 2 x the distance from mirror.. A mirror produces an image magnified by 1.5 when your face is 29 cm from the mirror. What is the radius of curvature? I thought it would be .29m x 2 = .58m... but that...

Hi, In two dimensions I am under the impression that the ricci tensor or the scalar curvature equals the negative of the fundamental tensor and the sectional curvature (K). I'd have written it out with the proper symbols but I am new to this forum and this isn't at least a complex question...

Hi, A particle is projeted with a velocity 'u' at an angle \theta with the horizontal. Find the radius of curvature of the parabola traced out by the particle at the point where the velocity makes an angle \theta/2 with the horizontal. I got u^2/gcos\theta/2 but my book gives a different...

In order for the universe to remain flat, doesn't the contribution to curvature by mass have to be canceled out by the contribution by dark energy? If the mass contributes to positive curvature, then dark energy would be there to make a negative contribution to curvature. And yet, without dark...

Find the curvature at the point P: f : [0;2] IR^2 , f (t) = 2t,4 −2t^3 , P(2,2) i subs 2x=0 then x=0 and 2y=2 then y=1 t=(0,1) then i perform the curvature calculation.however,i'm confuse that in this case i have to subs t=1 to get a value instead of zero. If the value t=(2 ,3)...

I need help in trying to explain to someone how gravity creates curvature and paths of particles are curved around this curvauture? like the sun on a trampoline and the Earth's path around it being bent as it orbits the sun. so why does the sun bend the space around it? and why does the Earth...

I am reading The Universe in a Nutshell by Stephen Hawking, a book everyone here has probably read, or at least heard of. In the first chapter, he talks about how the effects of acceleration and gravity prove the curvature of spacetime. I'll give you some exact quotes from the book to make it...

A concave mirror has a focal length of 10 cm. what is its radius of curvature?:eek: i have absolutely no idea how to solve this, please help:cry:, any advice is greatly appreciated:smile:

Ok, I'll try & lay the picture as best as possible. I'm on a spaceship & have a laser on the floor pointing towards the ceiling. When I'm not accelerating the laser shoots up & hits the ceiling. No problem there. If I'm accelerating at a fast enough pace the laser wouldn't go straight to the...

How is spacetime curved if the present gravity field is completely uniform and there are no tidal forces. Clocks at a same height would tick the same, at different heights (to the gravity source) would tick differently. But what about space? How is space curved in the absence of tidal forces...

Can an object be constructed in such a way that, when thrown WITH rotation in space, causes the object to curve in it's trajectory. Now, I'm not referring to "curve balls" in baseball, because a curve ball in space will not curve. Rather, I'm thinking somewhere along the lines of a "dumbell"...

I'm reading Advanced Calculus by Wilfred Kaplan 1952. He is demonstrating how to find the decomposition of the acceleration vector into its normal and tangential components. I'm following along until he replaces the magnitude of the derivative of the angle with respect to the distance traveled...

if gravity is a property of geometry of spacetime then does it imply that space is an entity in itself as Newton hypothesized, i mean if space is curved by a mass of a body and therefore creativg gravity around a particular radius then doesn't it imply that space isn't relative to masses as...

Given that Dark energy supplies negative pressure: Does it have mass? Does it curve space? If so, does it help to close the universe? Can something that has negative pressure also make space more closed? Does it affect time dilation? How do you achieve a flat universe when there seems to...

Hey guys was wondering if anyone could help me out :) Question))A Positive Charge Q is uniformly distributed around a semicircle of radius a. Find the electric field(magnitude and direction) at the center of curvature P. Basically it looks like a unit circle except the radius is A and we...

Is gravity a result of the curvature of spacetime, or is it the curvature of spacetime a result of gravity? Or something else? Thank you.

curvature on the earth? caused by the presence of a nearby massive object (like the Earth). but how does gravity act upon us? i got the idea of how it does in space. but earth? if it's a curvature, then what's keeping us on the ground. surely, there's no curvature on earth! can you explain...

I take it that there are various ways of curving spacetime with a desired value of curvature. Is there an overview or a run-down of the various metrics, their names, where they are applicable, and how they curve spacetime? For example linear acceleration curves space differently from gravity...

Hi guys ,I need help to find the radius of curvature for this exercice: A metal bar is 1.75m long with a coefficient of thermal expansion of 1.34*10-5K-1. It is rigidly held between two fixed beams. When the temperature rises, the metal bar takes on the shape of the arc of a circle. What is...

What does it mean by "shot wave length corresponds to high curvature of the wave function" ?

How do i find the number of independent components of the Riemann curvature tensor in D space-time dimensions. One is given that the Riemann tensor is an (2,2) irreducible rep of GL(4, \mathbb{R}) and obeys Bianchi I R_{[\mu\nu|\rho]\lambda}=0 Been trying this problem for 3 days and...

Hi, Question Some rearvier mirrors produce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is the mirror's radius of curvature if cars 20.0 m away appear 0.33x their normal size. My Answers The mirrors are...

I was wondering how to find the radius of curvature of a helix. If it's circling around the z axis, the radius of it's projection onto the xy axis is a circle of radius r. Let one full cycle of the helix around the z-axis cover a distance d along the z-axis, then what is R, the radius of...

Hello everyone, the problem says to: For the curve gien by r(t) = <1/3* t^3, 1/2 * t^2, t> find (a) The unit tagent vector; (b) the unit normal vector; (c) the curvature; Well it seems easy enough! the formula's are just derivatives for instance: The unit tagent vector says: T(t) =...

Hello everyone, I think i did this problem right, but I want to make sure sure. The directions are as fallows: (a) find the unit tagent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find curvature. Note: formula 9 is the one i have on my paper: k(t) = |T'(t)|/|r'(t)|; my...

Hello everyone, I'm trying to figure out the curvature of a line, First I'm suppose to make a hypothisis on what i think it would be, then I'm suppose to put a line in parametric vector form and find out really what the curvature of the line is. Well a line is pretty straight, so why can't I...

Today my teacher mentioned a past article in scientific american that dealt with the modification of reality due to relativity. According to her (and i am not sure this is true) light can be perceived in different places according to the position of different people. For instance, if i am...

Hello, I just learned how to do these types of problems, but I'm having trouble. Can some one direct me through this problem? Find the point or points on the curve which the curvature is a maximum for a. y=ex b. xy=1 any help is greatly appreciated. I really am stuck here!

for a curve defined by y=f(x) the radius of curvature is defined as [f""(x)/(1+f"(x))] power 3/2. I need a good neat & understandable derivation for that. can anybody show a web.

Next week in my multivariable class, we'll be starting curvature, and, nerd that I am, I looked ahead to learn it ahead of time. I can usually at least understand the basics of a new concpet by myself, but curvature really threw me off. Maybe my brain's not right for it, maybe the book sucks...

This is the first thought that I had a question about, but it is highly dependent on a specific model of the universe, so I asked whether or not my model of the universe is feasible in a previous post, "Model of the Universe (I)". I have tried searching on Google for an answer, but I am not...

Hi; Could someone please help me with the following question: The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 18.8 cm behind the mirror. What is its radius of curvature? (Use positive for concave and negative for convex). Would I...

we are doing forces and gravity , but what I don't understand is when the sun curves spacetime for the Earth to orbit this curvature, what causes it ? thanks in advance. roger

Hi, I was really hoping someone could help me... I have a beam, simply supported and I place 2 point loads on it (equidistant from either end). I measure a range of deflections (of the beam) using gauges as I increase the loads (always having the same load at each point). I measure these...

In Brian Greene's 'Fabric of the Cosmos', he describes three possible curvatures that space may have: positive curvature (like a ball or torus), negative curvature (like a saddle) or zero curvature (like an infinite flat tabletop, or like a Pacman video game screen). In his analogy to a video...

When Enstein developed tensor analysis because all the other math fell apart, there was another type of math that was developed to measure the curvature of space. What is it? How does it work?

An object is located 36 cm to the left of a biconvex lens of index of regraction 1.5. The left surface of the lens has a radius of curvature of 20 cm. The right surface of the lens is to be shaped so that a real image will be formed 72 cm to the right of the lens. What is the required radius...

The old 2D paper describing 3D curvature is a little lame because it uses gravity to describe gravity. You know, the little ball circling the 2D psuedo-black hole, well remove gravity and the ball would fly off the 2D paper, you can't use gravity to describe gravity. It would be like saying...

Those of you who know me know that my formal education is in physics, not mathematics. So hopefully you'll excuse the dumb question, but in what course would one learn about extrinsic and intrinsic curvature? I have books on tensors, differential forms, topology, analysis, and advanced...

I understand that the curvature is caused by the depression of a mass in the space-time surface. What I don't understand is what is causing this depression. For example, is it the bodie's resistance to the motion of the space-time surface? Or is it that the curvature is caused by the...

A quick question. In stewart, the curvature is defined as: \kappa = \abs(\frac{dT}{ds}) and it says that: "The curvature is easier to compute if it is expressed in terms of the parameter t instead of s, so we can use the Chain Rule to write: \frac{dT}{dt}=\frac{dT}{ds}...

The terms elliptic, hyperbolic and euclidean geometry are defined according to the sectional curvature, which is a generalization of the Gaussian curvature of a surface. Are there any restrictions on the sectional curvature for spacetimes in general relativity? The Ricci scalar, being a...

Suppose you have a tube made of nylon. It is filled with air. Obviously, the cross-section is a circle. Now, suppose that on the top and bottom of the tube, a length of rigid sheet metal is attached and does not permit curvature, so that the cross-section after inflation looks like this...

Is there a formula which relates the angle of a steering wheel from normal position (theta) and the radius of curvature (r) of the arc that an average vehicle moves through? (assuming power steering, since that's the most common) Such a formula would be useful in calculating centripetal...

I'm working through some questions on lenses, and I'm a bit stuck on this one involving radius of curvature. The part of the question I'm having difficulty with is The lens is made of crown glass of refractive index n=1.51. The radii of both surfaces is the same. What is the radius of...

Hey, when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field V , ie like this :- [\bigtriangledown_a, \bigtriangledown_b] = \bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a = V;_a_b - V;_b_a But...

hi how is space curvature around a mass. i mean what's its direction in real 3D space? [ i know it is simillar to a rubber sheet with a ball on it, but it is 2 dimentional. i want its real demonstration. just like real world.]

Is it true that space can be curved around and loop itself to a point in the past? If this is true, then time travel to the future and the past should be theoreticly posible. I'm trying to further uderstand relativity, this is why I ask. If we could travel to the past, maybe we can really see...

I have not been keeping up on current cosmology theory. Once was said that if you flew your "Spaceship of the Mind" X billion light years "thataway", and didn't stop or turn, you eventually would find yourself back where you started. The idea here is that 3-dimensional space is actually...

Space Curves --> Unit Tangent Vector and Curvature Here is the original question: Consider the space curve r(t) = (e^t)*cos(t)i + (e^t)*sin(t)j + k. Find the unit tangent vector T(0) and the curvature of r(t) at the point (0,e^(pi/2),1). I believe I have found the unit tangent vector...