Torsion Definition and 237 Threads

As I understand it, Riemannian geometry doesn't allow Torsion (a property of geometry involving certain permutations among the indices of Christoffel Symbols). Does this restrict the geometry of General Relativity (GR) to describing only a curved spacetime with the Riemann curvature tensor? Is...

Hi there, needing some help with a torsion spring application...I'm looking to use a torsion spring to load a carousel (which is about 400mm diameter, 100mm height and weighs about 2.5-3Kg) so someone will turn this carousel (onto a base) which will load the torsion spring...the spring will be...

Homework Statement A Bimetallic torsion bar consists of a steel core (Gs = 75 [GPa]) of diamter di = 25 [mm] around which is bonded a titanium sleeve Gt = 45 [GPa] of inner diameter di = 25 [mm] and outer diameter do = 40 [mm]. a) If the maximum sher stress in the steel is 50 [Mpa], what...

Homework Statement We have a round disc with radius of 10 cm and mass of 1 kg, suspended on a wire and lying on a thin (1 mm) layer of oil. We torsionally nudge it and we get some info out of it: At angular velocity of 10 s^{-1} the amplitude is maximal. At angular velocity of 12 s^{-1}...

Homework Statement I have been tasked with finding the angle of twist of the following component: Hollow tube 40mm diameter, 2mm wall thickness, with a 2mm cut along its length (see image), x=2mm. Homework Equations Please see attachment for equations. The Attempt at a Solution...

Hi, Everybody: I am trying to understand torsion and relative cycles in a more geometric way; I think I understand some of the machinery behind relative cycles (i.e., the LES, and the induced maps.), and I understand that by ,e .g., Poincare duality, in order to have torsion in...

Homework Statement I have been having a little discussion with a friend. We both know that for a spring/damper system in parallel like shown below, the associated free body diagram is correct. http://img337.imageshack.us/img337/2023/para0.jpg But when it comes to the same system in...

Homework Statement 1. Prove the equations. 2.Two solid circular shafts are connected by 5cm and 25cm-pitch-diameter gears as shown in Figure 1.2 below. The shafts are assumed to be supported by bearing, as such bending is negligible. Find the angular rotation at end D with respect to end A...

Homework Statement [PLAIN]http://img821.imageshack.us/img821/1089/64194000.jpg The attempt at a solution How should I get started on this one?

Homework Statement [PLAIN]http://mityaka.com/users/kolodny/img/lagprob.png Homework Equations L = T - V T = \frac{1}{2}*m*U2 Vs = \frac{1}{2}*k*x2The Attempt at a Solution I worked out the equations of motion as: FL = m*\ddot{y}+k*y-k*b*\theta FL*e =...

Torsion question can anyone help? Homework Statement For a power transmission system, a solid steel shaft is required to transmit a torque of 2000 Nm. The limiting factor is that the twist of the shaft should not exceed 5 degrees for each metre of the shaft length. The shear modulus G is 75...

I am looking at this building and wondering how building torsion is resisted as well as what role the roof diaphragm plays in it, hence what would be the shear force and bending moment diagrams...

So, is there a torsionon? I tried to sort out something, but the only thing I could find was paranormal stuff, unfortunately. So, I at least I came up with this, although no mention to torsion as a particle: http://arxiv.org/abs/gr-qc/0505081 (equation 4) Physical effects of the Immirzi...

Homework Statement A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation. With what period does it now oscillate...

Homework Statement A shaft fixed on both ends is shown below. It is made of a steel tube, which is bonded to a brass core. A torque T_D is applied at location shown. The tube is fixed at both ends. [PLAIN]http://img202.imageshack.us/img202/2940/problem2eb.jpg Show that the fraction of...

If our spacetime has torsion, will it violate the conservation of angular momentum? Thx

Homework Statement How would you find the energy efficiency of a torsion catapult ? (one i built for project) I have the Force at which I am pulling the arm. F = 20N also the angle from origin to the point of release ( or when the ball leaves the arm) Theta = 50 degrees...

the foollowing hollow shaft has a torsion applied to it so that the plastic area reaches the inner radius, what is the magnitude of the maximum residual shearing stress? http://lh3.ggpht.com/_H4Iz7SmBrbk/S9XK9ZwAbQI/AAAAAAAACFU/ueYSDTK5qMM/s800/Capture.JPG i don't see why there should...

Hi, I was wondering if anyone could help me with this differential geometry question I've been struggling to find information on. I (at least very roughly) understand the relationship between the Frenet-Serret curvature of a curve and the Riemann curvature of a general n-dimensional manifold...

Hi, I'm reading this piece from George Cain & James Harod's multivariable calculus material. Section 4.3, which is about Torsion, says this: I don't understand how he deduces dB/ds is perpendicular to T? Where did I get lost? Following the paragraph, it seems to me that T and N...

Hi every one. I just wonder whether using Ix+Iy = J is a suitable method to calculate the Torsion Constant of a plate girders (full penetration butt weld at connection section) Since, as stated at wiki, the polar moment of inertia is only identical to J for circle tube and rod. p.s. is...

Hello, I was wondering whether it is possible or not to define Killing vectors in a manifold with torsion. As a first approach I was reasoning like: Taking as definition of killing vectors, a vector field that: any set of points when displaced along a Killing integral lines, by equal...

the beam below is subjected to a single torque of Mt=10KNm at its centre, G=80GPa find the distribution of the torque between the 2 components of the central cross section what i have done in similar questions (where i have had one free end) i have chosen T1 and T2 - the relative...

Hi everyone, What I'm looking for are good examples demonstrating torsion in homology. The basic example I know is RP^2, but I suspect there are many more good examples out there. I am interested in the topic both for fun and as part of my research. In addition, I will be teaching a class...

What role does "torsion'' play in string theory? In general relativity we assume that connection is torsion free. However from a purely geometrical viewpoint, the concept of torsion can not be ignored (theoretically) and in string theory, it is said that "torsion" does play its role. Can...

for the folowing beam made up of a top half where E=210Gpa and a bottom part where E=70Gpa a=0.2m t=0.024m, b=0.04m i am asked a few different things a)to find the shear forces and bending moment arrays in the beam b)plot the normal stress as a function of the moment, how do...

Each of the two aluminum bars shown is subjected to a torque of magnitude . Knowing that , determine for each bar the maximum shearing stress and the angle of twist at B. Answers: a) 40.1Mpa 0.6630 degrees b) 50.9Mpa 0.9510 degrees my...

Hello all, I need some desperate help. I have a product that is mounted on four corners with 1/4-28 bolts with a shank diameter of .25. The product is mounted to a vibe table and shaken at 20g in each of the three axis. I am currently analyzing the stresses induced in the fasteners in order to...

Hello I recently got handed this problem and I had a fair idea on how to go about it or so I thought! My only problem is I do not know how to find d? I would be grateful if someone could show me how to find d and show me the equation used Thank you Homework Statement A steel shaft 3m...

I was watching a show about 2012, and someone named Richard Hoagland was giving theories about torsion fields. He was talking about mass changing due to rotation, and he could measure this by measuring frequency of the tuning fork of an accutron watch. He performed an experiment similar to the...

Homework Statement Consider a hollow drive shaft of length L, inner radius b, outer radius a. A constant torque is applied (we can assume one end of the shaft is fixed because we're applying a constant torque T regardless of the angular velocity of the shaft). We know material properties of the...

A horizontal hollow rectangular mild steel tube 30mm x 50mm with 4mm wall thickness and 350mm long, which is part of a frame has 2 lengths of studding 300mm long , 180mm apart and equidistant from the ends, welded to the 50mm face of the tube. A total perpendicular load of 400Kgs is...

Homework Statement Hello, I am writing up a lab for a torsion test that we performed on mild steel (ductile material) and cast iron (brittle material). For each of the materials, we must find: • For Mild Steel: - Torque vs. Angle of Twist per unit length. - Shear Modulus - Shear Yield...

Homework Statement In the experiment, you will study an oscillator called a "torsion pendulum." In this case, the restoring "force" is the torsion constant of the wire that suspends the weight X and the inertial term is the rotational inertia of the suspended mass. You will compare the periods...

Some time ago someone introduced me to the following scenario. Imagine you ship loads of oil rig pipes into space, and you assemble them to a length of many kilometers, and you start that long pipe spinning on its long axis. You add vibration damping, to get rid of any transverse, longitudinal...

Hi every one. As Steel Frame Manuel mostly discribe the force analysis in vertical loading, I wonder how can i solve the following case, a member that suffer torison. Is there any reference book you might suggest me to read ,too? Thanks for your kind help. The attached are the cases...

Notations: M denotes an abelian group under addtion R denotes a commutative ring with identity ann(?): Let M be an R-module and r∈R v∈M, then ann(v)={r∈R | rv=0} Terms: R-module: a module whose base ring is R torsion element: A nonzero element v∈M for which rv=0 for some nonzero r∈R...

I know that GR is essentially a Riemann theory w/o Torsion; the Levi-Cevita-Connection is symmetric and therefore the torsion vanishes. What happens when fermions are included? Does the spin-connection still guarantue that the covariant derivative comes with a torsion-free connection...

hkhk if G= Z4 x Z what would be the torsion group T(G)? and what is the factor group of G/ T(G) ?

Homework Statement Let G be a finite abelian group and let #(n) signify the number of elements x in G which satisfy x^n = e. Find the torsion coefficients of G when #(2)=16, #(4)=32, #(3)=9, #(9)=81 and x^36=e for all x in G. Homework Equations The Attempt at a Solution I really...

I'm curious as to how you would write a Lagrangian for a torsion pendulum. Say you've got some disc that has mass and it's attached by a spring with spring constant k to a stationary "ceiling" of some kind and has gravity acting on it downwards. So, not only has it got rotational energy, but...

Homework Statement let there be a beam connected to a wall at one end (left). in the other end there is a cylinder attached to the beam with an inertia moment of I0 the cylinder is then connected to a torsion spring which is connected to a right wall the beam (cantilever) has a inertia...

Energy "lost" in rolling, sliding and torsion Hey everybody, I have a question concerning three states and the state of energy in them. 1. Rolling 2. Sliding 3. Torsion For example: If I have a steel cylinder with diameter d on an axis (no friction in the axis) rolling horizontally over a...

I am reading a book which says that if the components of the connection vanishes then the torsion and curvature tensors vanish. Now, I understand how this happens with curvature tensor, but I don't see how torsion tensor would vanish. Torsion tensor: \tau (X,Y) = D_X (Y) - D_Y (X) - [X,Y]...

Homework Statement Shaft AB is fixed at point A and is subjected to a torque T = 2.5 kN·m applied at point B and an axial force P = 30 kN applied at point C. The actual shaft specifications (type of material, prismatic / changing cross sections are left up to us and is NOT the point of...

Homework Statement Homework Equations tao=Tc/J theta=TL/JG The Attempt at a Solution I got the torque of the motor as 210,085lb-in Then I converted the 4* to .698 rad From there I plugged it into the equations. I solved for T from tao=Tc/J then plugged that T into the...

Hello, Does anyone have any suggestions on how to approach torsion of a thin-walled thin ring/oval? so if this is a top view of the ring: O then the torque would be applied with the torque vector pointing as O--> (ring is fixed at the opposite end).

please explain the concept of Torsion rigidity giving examples.

I'm trying to design a simple torsion spring catapult to launch a 0.15kg ball at a velocity of 35 m/sec at the moment of separation. The ball will be in direct contact with the unrestrained end of the spring. As a starting point, I'm planning a 0.3m length for that "arm" end of the spring as...

Homework Statement The question is shown in the attached picture. I know how to do the first part fine,and i know how to do the second part but i keep getting the wrong answer (answers are on the back of the sheet)Homework Equations tau/r=T/J (tau = shear stress, r = radial distance from...