When is torsion negative

In order to calculate the maximum shear stress on a rod due to torque the equation below would be used. Notice from equation 2 that there is a variable J called Polar moment of inertia. The reason why the polar moment of inertia is included in the equation above is because it represents the ability of the specific shape to resist torsional deformation. This value has no dependence on the material properties of the given object.

To calculate the polar moment of inertia for a circular rod equation 3 would be used. For the above equation r i goes to 0 if the cylinder is solid. If the cylinder is a tube r i is the inner radius of the tube.

For any applied stress to an object there must also be a resulting deflection of the object. In the case for torsion it would be a twisting motion called the angle of twist. The resulting equation can be seen below. If torsion is positive, the curve "turns" to the side to which binormal vector points.

If torsion is negative, the curve "turns" to the opposite side. A curve "can make this choice" at a given instant, only if its binormal vector at that instant is well defined.

For torsion in the case of a left module over an associative ring cf. Torsion submodule. Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. A curve with vanishing torsion at each point is a planar curve. How to Cite This Entry: Torsion. Encyclopedia of Mathematics. This article was adapted from an original article by E.

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