Torsion Definition and 237 Threads

Using Frenet equations, find an expression for the torsion in terms of time derivatives of the position vector. The Frenet Equations are \begin{align*} \frac{d\hat{\mathbf{u}}}{ds} &= \frac{1}{\rho}\hat{\mathbf{n}}\\ \frac{d\hat{\mathbf{b}}}{ds} &= -\frac{1}{\tau}\hat{\mathbf{n}}\\...

Consider the case of a right circular helical curve with parameterization \(x(t) = R\cos(\omega t)\), \(y(t) = R\sin(\omega t)\), and \(z(t) = v_0t\). Find the curvature and torsion curve. http://img30.imageshack.us/img30/7828/gwi.png We can then parameterize the helix \begin{align*}...

Homework Statement The problem is regarding the question on the attached file called 'QUESTION3.png' This is urgent so please reply if you can. Homework Equations The attempt is in the file attached. Is my procedure correct? Am I missing something or is something wrong? Also, how do...

In the fig. attached below,a circular bar is subjected to torsion. A point is considered on the surface of the bar(denoted by point 1). The shear stresses are shown . Why don't we take one of the stresses in the radial direction??

Homework Statement The solid shaft is made from brass that has an allowable shear stress = 100 MPa and a shear modulus of elasticity G = 39 GPa. The length of the shaft is L = 2 m, and over the length of the shaft the allowable angle of twist is θ = 0.10 rad.the shaft is subjected to a...

hello everyone! so as the title suggest, i wonder if anyone would have any idea to design a simple experiment to determine the bending strength and torsion of a plastic ruler. it doesn't need to be extensive, as the value of the strenght itself isn't important. i just want to know e.g how...

I don't really understand the point in Curvature and Torsion, I am wondering if someone could explain them to me. Thank you for your kindness: Why do mathematicians need Curvature and Torsion? What are their main uses??

1. Problem statement. 2. Relative formulas http://en.m.wikipedia.org/wiki/Torsion_spring 3. Attempt. Part a) Since I am given the arc length S and radius, I use the equation s = r(theta) and I solve for theta, with r being the length of the rod and the addition of the radius of the ball...

Background for the question: In standard GR the equation of motion of a (classical) particle is a geodesic. A geodesic is a curve along which the tangent vector is parallel transported. If the tangent vector is denoted by V this condition is \nabla_V V=0 In components this is...

Homework Statement A thin metal disk with mass 2.00E-3kg and radius 2.20cm is attached at its center to a long fiber. The disk, when twisted and released, oscillates with a period of 1.00s. Find the torsion constant of the fiber. Homework Equations a) ω=sqrt(κ/I) b) f=1/(2π)...

Here is the question: Here is a link to the question: Consider the curve r(t)=<sinh t, cosh t, t>? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Interesting theory for consideration: Cosmology with torsion: An alternative to cosmic inflation http://arxiv.org/abs/1007.0587Nikodem J. Poplawski (Submitted on 4 Jul 2010 (v1), last revised 2 Nov 2010 (this version, v2)) In this work, we considered the ECKS theory of gravity which is the...

Hello Everyone, I am after an expression for the torsion stiffness constant of a rectangular hollow section (RHS) with varying wall thickness. I have done some research into finding an expression that allows for four varying wall thicknesses but have not found anything as of yet. The only...

Homework Statement Determine maximum distance an one ounce projectile can be launched with a torsion spring catapult. Homework Equations E = F * d = 1/2 * m * v02Note: Theta is the measurement of how far the lever arm is being pulled back. Am I missing something?

This is a WELDED PART, the welding is marked in the drawing at the left side. http://img94.imageshack.us/img94/5414/torsionp.jpg My lecturer claims that the moment here causes torsion! How come? I can't imagine torsion working without a 3D model...

Homework Statement the statement: You are taked to design a 2m long shaft which is to be manufactured either as a solid circular bar or a circular tube. the shaft is required to transmit a torque of 100Nm without exceeding the alloqable strength of material. Find the required outer...

Torsion has propped up in a couple of recent threads, but none of my texts really cover it well. Does torsion make parallel transport direction dependent? I.e. if we parallel transport some vector v "forwards" along a curve, and then "backwards" along the very same curve to its starting...

Homework Statement It's not exactly a homework question, just want to see if i have the right concept in drawing free body diagrams See attached Picture. In case 1, the object is fastened on plane x-z and the rectangular block is fastened to the T-block in y-z plane. Will the force be...

Is frame dragging in GR the same as torsion in curved spacetime?

How did gastropods evolve torsion? I have looked all over. There doesn’t seem to be any clear idea of what torsion does now, let alone what purpose it served long ago. There was a hypothesis (Garstang’s hypothesis) that the veligar larvae developed torsion so they could pull their...

Hi, I have got experimental data for a steel material for a cyclic test perfoemd in the following scenario: 0-1% Torsion followed by 0-1% strain Tension followed by 1-2% Torsion followed by 1% to 0 % compression followed by 2 to 3% torsion followed by 0 to -1% compression...

This is really more of a differential geometry question than a GR question. Is it possible to have torsion in two dimensions? I've seen statements implying that torsion is only of interest in 3 or more dimensions, but I don't see why. My understanding is that in two dimensions, you could not...

I'm very confused regarding this problem and i will explain in it in details ,hoping anyone can explain the reason For example we have a bolted connection subjected to torsion ,the bolts will have extra shear in the plane also when i strike a a slab of small building with lateral load(assuming...

Hi all, I am working through Visser's notes http://msor.victoria.ac.nz/twiki/pub/Courses/MATH465_2012T1/WebHome/notes-464-2011.pdf section 3.5 onward. I am trying to differentiate between the torsion and the Riemann curvature tensor in a heuristic manner. It appears from "Geometric...

torsion --> covariant deriv of det(g) non-zero? I am missing something here. This paper makes the case (on page 5) that for non-vanishing torsion, the usual invariant volume element \sqrt{-g}d^4x is not appropriate because the covariant derivative of sqrt(-g) is non-zero. This perplexes me...

Hi all, I am simulating torsion tests (after being successful with tension and compression tests). For tension and compression, I got a good comparsion with experimental and behaviour in tension is same as in compression (of course leaving the necking part). For torsion tests, I have...

Okay, so I'm studying for a Mechanics of Materials final at the moment, and I am reviewing the chapter on torsion. I was reading through the given formulae, and I stumbled across one that I could not fully visualize (or simplify): the formula for gamma. Based on my understanding and from...

I’ve been struggling with this for quite some time and will be grateful if someone can help me. I have got the data for some tension and torsion tests performed on standard specimen- the tests were done by someone else- not me. I’m trying to do a material modelling based on the tests...

New here, sorry if I'm in the wrong place or unclear, etc. I've been looking at torsion on solid plates and the torsion constant. I was wondering how to handle the torsion constant on a plate of changing cross section (e.g. there are holes drilled in it, changing the area of the cross section...

Hi, How would I go about finding the spring constant of a bundle of nylon rope acting as a torsion spring? I know the length. I don't know the width of the bundle. When twisted I wanted roughly 6cm diameter (is that a wrong method)? I ll be twisting it by 1080 degrees. When twisted...

Hello, I'm a student of mechanical engineer and currently doing a project on "fabricating a torsion test equipment". I'm just wondering about my torque calculations. My design is quite simple, consists of: - angle iron (frame) - torque angle gauge (to measure angle of twist) - 2x...

Suppose we have either a massive or massless complex field in 3 space and one time dimensions. Suppose we force (or drive) the field on the surface of a small sphere with a function like, exp(-t^2)*exp(-iωt) I'm guessing the result of such forcing will be a circularly polarized wave that...

1. Homework Statement Compute angle of twist of one end relative to other if a torque of 850 lb-in is applied uniformly along the length. Shaft has two flats (not just the 1 pictured!) 1.25 " is measurement across flats. Homework Equations J = C r^4 The Attempt at a Solution I had...

Homework Statement A drive shaft tube for a rear wheel drive high-performance sedan requires a lighter weight unit than one made from conventional steel. The requirements are that the applied torque be 814 N-m (600 ft-lbs) the factor of safety be 2 or more and the maximum angular displacement...

Homework Statement Question Assuming the torque and maximum shear stress values to be the same for both shafts, determine the size of a suitable soild shaft which could be used instead of the hollow shaft. Information/Data Known Firstly, a previous question - A ship's propellar...

Homework Statement http://img820.imageshack.us/img820/3373/torsionquestion.jpg Homework Equations (In the solution) The Attempt at a Solution I got M(max) and d correct. I can't get the angle. But I'm using the formula exactly as is. What's wrong...

Homework Statement http://img840.imageshack.us/img840/736/mmaterials.jpg Homework Equations http://img18.imageshack.us/img18/8739/releq.jpg The Attempt at a Solution http://img845.imageshack.us/img845/7017/pitul.jpg The answers turn up (a) 56.6 MPa and (b) 36.6 MPa so I'm...

Homework Statement i did my experiment on torsion pendulum and there is a graph that i am supposed to draw ( C as a function of 1/L) where C is the tosion constant and L the length of the wire after that they give me a formula C=1/32L *∏*G*a^4 where G is called the modulus of rigidity and a...

I have recently done a lab at university which studied the effects of combined bending and torsion. It was conducted using a Hi-tech HSM.11 piece of equipment. We applied loads at a series of angles, 0deg, 45deg and 90deg. We then worked out our principle stresses and yields. One of the...

Hi, I'm reading this wikipedia article on the metric connection, and it says that the Levi-Civita connection is a metric connection without torsion. If the metric connection is defined so that the covariant derivative of the metric is 0, how can there be torsion? Doesn't this condition force the...

Homework Statement http://www.mathhelpforum.com/math-help/attachments/f6/22423d1317129472-curvature-torsion-untitled.png The Attempt at a Solution What I did was I calculated the unit vector for dN/ds={.21i+0.91j-0.42k}/ sqrt(.21^2+.91^2+0.42^2)=.205i+0.889j-.4102k then, I...

Homework Statement I need to calculate the spring constant of a torsion spring. Turns : 20 Mean Diameter : 6mm Wire Diameter : 2mm Material : ASTM A228 Arm Length : will be negligible, as they will be fixed Orientation : Arms inlineHomework Equations k=\frac{Ed^4}{10.8DN} The Attempt at a...

Looking to figure out the allowable stress (psi) of a shaft which has two pin holes in it on the transverse axis of the shaft. tau = allowable stress, psi T = torque, in-lb c = distance from center of gravity to extreme fiber J = polar moment of inertia D = diameter of the shaft d =...

In 3D the torsion  measures how rapidly the curve twists out of the osculating plane in which it finds itself momentarily trapped. So in 4D, would torsion measure how rapidly a curve twists out of the osculating 3-hypersurface in which it finds itself momentarily trapped? Or torsion of a...

I was reading something about the Cartan (vierbein) formalism in GR, in which the connection is allowed to have torsion, and it got me interested in the Einstein-Cartan theory. Apparently both GR and Cartan theory with torsion should give the same experimental results in vacuum, what I would...

Homework Statement A turbine shaft is to transmit power at 240 rev/min. If the shaft is 1 m external diameter and 25 mm thick and the maximum shear stress is limited to 69 MPa, find the power transmitted. Homework Equations The Attempt at a Solution T=J*stress/r =...

Mentz114 posted this interesting link: http://arxiv.org/abs/gr-qc/0011087 Teleparallel Gravity: An Overview Authors: V. C. de Andrade, L. C. T. Guillen, J. G. Pereira Abstract: The fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties...

If torsion = anti-symmetric part of the connection coefficients, and \Gamma_{\alpha\beta\gamma}=\frac{1}{2}(g_{\alpha\beta,\gamma}+g_{\alpha\gamma,\beta}-g_{\beta\gamma,\alpha}) then doesn't the metric have to have an antisymmetric component? The first two terms on RHS are together...

A steel rod like the one shown in the attached picture is fixed from one side and increasing amount of torsion is applied on the other side. Eventually, the rod breaks. Now it will obviously break from one of the two chamfered locations, where the middle portion of the rod with the smaller...

Hiya friends, so i have a little problem, A shaft is made from tube 25 mm outer diameter and 20 mm inner diameter. The shear stress must not exceed 150 Mpa. Calculate the maximum torque that should be placed on it ok so we have T/J = tau/r so T = (tau/r)*J - this should give me my...