In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements. A torsion module is a module that equals its torsion submodule. A module is torsion free if its torsion submodule is reduced to the zero element.
This terminology is more commonly used for modules over a domain, that is, when the regular elements of the ring are all its nonzero elements.
This terminology applies to abelian groups (with "module" and "submodule" replaced by "group" and "subgroup"). This is allowed by the fact that the abelian groups are the modules over the ring of integers (in fact, this is the origin of the terminology, that has been introduced for abelian groups before being generalized to modules).
In the case of groups that are noncommutative, a torsion element is an element of finite order. Contrarily to the commutative case, the torsion elements do not form a subgroup, in general.
I was required to calculate the torsional stresses on these welds (in green) with the point of rotation G. However this doesn't fit any case in Shigley's so I'm at a loss as to how I should have calculated this. As advised by the teacher, I ended up replacing the keys being welded with full...
I have tried to draw a force diagram to illustrate the problem. Suppose I have a 2m, 100kg uniform rod with wheels at the bottom. Center of mass is middle of rod. I want to accelerate this rod horizontally while it remains perfectly vertical (constant angle). But the force is coming from a rod...
Hi,
I've been doing a course on Tensor calculus by Eigenchris and I've come across this problem where depending on the way I compute/expand the Lie bracket the Torsion tensor always goes to zero. If you have any suggestions please reply, I've had this problem for months and I'm desperate to...
As I understand it, parallel transport of a vector around a closed loop on a manifold can lead (in the tangent space) to 1) an angular change, given by the Riemann curvature tensor or, 2) a translational defect given by the Torsion tensor.
I can see how the looping on the curvature of a 2D...
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As you could see the moment try to make beam to rotate in the support plane with the wall which mean for me this moment is on the Z direction but the longitudinal axis is the X direction and I know that for a moment to be torsion it needs to be in a longitudinal direction, but the...
Summary:: trying to calculate the torsion but couldn´t understand the solution
Greetings
I´m trying to understand why the multiplied the Force by a/2 to find the torsion in te point c
thank you!
For a Prandtl stress function to be valid, it must be zero on the boundary. For a circular bar, both of these work:
$$\phi_1 = C\left(\frac{x^2}{r^2}+ \frac{y^2}{r^2} - 1\right)$$
$$\phi_2 = C \left(x^2+ y^2- r^2\right)$$
But performing the integration for the internal torque M gives...
I have a crazy idea to make a 4 motor EV, but ran into an issue: the motors I want to use have a gear reduction (transmission?) That has a differential built into it. I only need to use one side of each, but I don't want to weld or otherwise destroy the other side of it. (That way I can...
Hi,
solid elements used in FEA don't have rotational DOFs so normally it's not possible to read the angle of twist from simulation involving torsion. Some programs allow the transformation of results to cylindrical coordinate system but it's not always the case. From what I've heard, it's...
I was trying to compute the equations of motion for the spin ##\omega_{\mu ab} ## connection from the Einstein-Palatini action
$$S := \int d^4 x e^\mu{}_ae^\nu{}_b R_{\mu \nu}{}^{ab}.$$
I managed to get the variation wrt. the connection to the form
$$ \varepsilon_{abcd}\varepsilon^{\mu \nu...
I am trying to design a small box with a hinged door/lid that opens with a torsion spring.
When closed, the door will latch onto a mechanism where the open button is, and when the button is pressed this mechanism will slide away, removing the latch out of the way so that the door can fly open...
Dear Everyone：
Q：
Please help me to understand why the torque of external load to the centroid is different from the torque of internal shear flow to the centroid in the asymmetric beam?
Attached please refer to the following link for more details.
Question version
Original version
Thank you...
I recently came across a paper (referenced below) containing the statement that:"The differential form notation is much more concise and elegant than the tensor notation, but both contain the same information.", and the paper left me with a desire to understand the notation of differential...
I was watching a lecture that made the conclusion about the torsion being equal to zero necessitated that the path was planar. The argument went as follows:
-Torsion = 0 => B=v, which is a constant
-(α⋅v)'=(T⋅v)'= 0 => α⋅v= a, which is a constant (where α is a function describing the path and...
Hi,
I'm designing a small container with a spring loaded hollow rectangular lid. I want the lid to open when a button is pressed, so I have a torsion spring at the hinge. I want to know if the spring I selected is able to open the lid and also how long it would take to open 90°.
Below is a...
I read this paper where if you take the alcubierre metric calaculations while including torsion in GR you get positive energy spin requirements instead of exotic matter. Here is the link: https://arxiv.org/abs/1807.09745
Could it be because a spinning quantum vacuum will be less stiff like a...
Let's say we have any two covariant derivative operators ##\nabla## and ##\nabla'##. Then there exists a tensor ##C^{\alpha}_{\mu\nu}## such that for all covariant vectors ##\omega_{\nu}##,$$\nabla_{\mu}\omega_{\nu}=\nabla'_{\mu}\omega_{\nu}-C^{\alpha}_{\mu\nu}\omega_{\alpha}$$
Now I'm quoting...
Hi guys,
I am working on design where I am using a torsion spring. And I need make an analysis and see the deflection of the walls. How can I calculate the forces that applied from Spring's legs to walls.
Thank you all in advance.
Hello,
I found an integral to calculate the torque from the applied torsional shear stress, and I didn't find an explanation of how this integral is deviated. Where does it come from? Could someone explain?
T = ∫τ⋅r⋅dA = ∫τ⋅2πr⋅dr,
where T is the torque and τ the shear stress.
Thanks a lot!
Let us consider the massless homogeneous helical spring with the infinitesimal wire diameter d and wire length l. We denote the spring radius as R. Now we consider the curvilinear spring section of length dl. We draw radii from the spiral axis to the centers of the end cross-sections of this...
Hello
I would like some feedback about a problem. The idea is to calculate how much the angled bit of this beam moves things to account for are deflection and torsion. Did i miss anything?
Underlined with red are the displacements in millimeters.
In the picture the dotted line is the axis that...
I have a technical problem.
1. Accordingly to historical E.B. Christoffel’s work (I think year 1869), (Christoffel’s) symbols are symmetric in the two (today writing) lower indices.
2. These symbols have been introduced when studying the preservation of differential forms of degree two. The...
Hi,
I analyzed various open cross-section (I, T, L, C) bars using FEA to find maximum shear stress and twist angle. Now I would like to compare these results with approximate hand calculations. Just out of curiosity. However it's not easy to do it analytically. I know about a method of dividing...
I am struggling through a problem in one of my designs and would appreciate some help.
Please refer to the image attached.
Problem Description:
S = Torsion spring
F = fixed point
T = tire
A tire is attached to a torsion spring through an arm as shown in the image. The torsion spring has one...
Homework Statement
The torsion balance shown in the figure consists of a 40 cm long bar with lead balls with a diameter of 2 cm on each end. The rod is hanging by a 100 cm long silver thread with a diameter of 0.5 mm. When two bigger lead balls (density = 11.4 g/cm3) with a diameter of 30 cm...
Homework Statement
I've got a flywheel of Inertia = 0.0019302kg/m^2 (found via solidworks), when a torsion spring is released, a force of 10N acts on the wheel via astring attached 0.065m above and 0.0325m to the right of the wheel's axis at an angle of 40 degrees.
Homework Equations
What is...
A recent article in Smithsonian magazine about knitting geometric forms stimulated the following question:
In the above, knitted Moebius strip, there are areas where the material is twisted (seen in front) and areas where the material is flatter/less twisted (seen in back). So far as I can...
I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ...
I am currently studying Chapter 10: Introduction to Module Theory ... ...
I need some help with an Exercise 8(c) of Section 10.1 ...
Exercise 8 of Section 10.1 reads as...
I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ...
I am currently studying Chapter 10: Introduction to Module Theory ... ...
I need some help with an Exercise 8(b) of Section 10.1 ...
Exercise 8 of Section 10.1 reads as follows...
Homework Statement
Homework Equations
maximum torsional shear stress = (Torque*radius)/polar moment of inertia
The Attempt at a Solution
I am lost on equation(4-14), I looked through the textbook but didn't find a derivation.
Hi guys,
I am working on design where I am using a torsion spring to hold a certain load.
How can I calculate if the spring I am designing is strong enough to hold the load and prevent it from slipping down?
This is music wire 2mm diam spring, 90deg travel, 60mm legs. Please let me know if I...
Homework Statement
A torsional pendulum consists of a disk of mass 450 g and radius 3.5 cm, hanging from a wire. If the disk is rotated through an angle of 45o and released from rest and oscillates with a frequency of 2.5 Hz, what is the torsion constant of the wire?
A :
1.7 x 10-3...
Homework Statement
Homework Equations
Angle of twist = TL/JG
The Attempt at a Solution
T & L is inversely proportional.
But how can i start attempt the question?
I think it this way: like moment=L*F, and torsion torque is like force, angle of twist is similar to moment (as TL are also...
Hi, I'm struggling with this question on an exam pastpaper. I have attached the question and worked solutions below and i am stuck on Q10 c). I'm not sure how they knew that the torque is constant along the whole shaft. I thought a stepped shaft has different torques for its different sections...
Hi, below i have attached a exercise sheet question with the solution, however i don't quite understand it. In torsion, the maximum shear stress of a shaft is determined using the max radius of the shaft. Also, when comparing two sections, the one with the larger radius gives a higher shear...
Homework Statement
A rectangular Cross-section beam, 20cm deep by 10cm wide, is subjected to a maximum bending moment of 360kNm
A) Calculate the second moment of area of the beam cross-section
B) what is the maximum stress in the beam under this load
C) if the value of E for the beam of...
Can torsion angles were affected by repulsive effect of aminoacid interactions between side chains?
Can torsion angles were affected by hydrophilic or hydrophilic interactions between side chains?
I know that protein levels were affected by them but torsion angles is suspicious for me
Homework Statement
We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes.
Homework EquationsThe Attempt at a Solution
So I'm reviewing some stuff...
How spiral torsion spring (used in mechanical watches to store energy) works? physics behind it ? ... I googled it but haven't got a clue. Where should I look for proper and detailed info.
In the Feynman Lectures on Physics, Feynman explains the curvature of spacetime by drawing a rectangle in spacetime, see
http://www.feynmanlectures.caltech.edu/II_42.html Fig. 42.18
First waiting 100 sec and then moving 100 feet in height on Earth's surface results in a different situation...
Please bear with me, I am trying to design a shaft that will be under torsion. I do not know the diameter of the shaft and I would like to be able to calculate it by the things that I do know about the system.
There's a 15HP 3 Phase motor running at 85RPM [there's a gearbox]
This will be...
Hi everyone,
I am reading Sean Carroll's note on gr and he mentioned metric compatibility.
When ∇g=0 we say the metric is compatible.
However from another online material, the lecturer argues ∇ of a tensor is still a tensor,
and given that ∇g vanish in locally flat coordinate and this is a...
Homework Statement
A specimen tested in a simple torsion testing machine , the specimen was 12.5mm in diameter and the angles were read over a gauge length of 0.75m Determine the modulus of rigidity of the material taking the torque T as 4.5Nm and the angle of twist as 4.0 degrees
Homework...
Homework Statement
A solid and hollow shaft of the same material must transmit the same maximum torque. The diameter of the solid shaft is 203mm and the outside diameter of the hollow shaft is to be 216mm.
a) Determine the inside diameter of the hollow shaft. (answer = 138.7mm)
b) What...
Homework Statement
Homework EquationsThe Attempt at a Solution
I feel I did something wrong, but not sure where is my problem. I don't feel conformable on number 26 and 27 and 29, can someone please tell me which answer is incorrect and any tip on solving it would be greatly appreciated!
I have built a torsion wheel catapult (Mangonel) for an assignment,and I need to do some theoretical calculations about the displacement, velocity and time of the projectile, the problem is I don't know how to calculate the spring constant without the displacement of the spring (x) and i don't...
One way to see that spacetime is curved is to try and draw a "rectangle" in spacetime (see the figure in the Feynman lectures, ch 42.7): If I wait for 100 seconds and then move upwards on earth, I end up at a different point in spacetime than when I first move upwards and then wait for 100...
I have some conceptual doubts about shafts subjected to torsion. When studying Strenght of Materials, to find stress and strain in power transmission shafts, we consider that one of the ends of the shaft is fixed, with all degrees of freedom restricted, and the other one is receiving torque. I'm...
This is probably simple for an engineer, but I’m a zoologist and analytical chemist and so I would rather ask those who know.
I have camera traps out on the African bush, that are monitoring the responses of leopards to artificial scents. The cameras are in steel boxes to protect them from...