Torsionrelated

Torsionrelated refers to topics and phenomena connected with torsion, the concept of twisting or the presence of finite-order elements in algebraic structures. The term spans multiple disciplines, including mathematics, physics, engineering, and chemistry, reflecting both geometric twisting and algebraic order.

In mathematics, torsion has several meanings. In group theory, a torsion element has finite order, and the set of all torsion elements forms the torsion subgroup of a given group. In topology and algebraic geometry, torsion subgroups appear in homology and cohomology groups. In differential geometry, torsion of a connection measures the failure of covariant derivatives to commute; the Levi-Civita connection is torsion-free, while more general connections may possess torsion tensors that influence curvature and parallel transport.

In physics and geometry, torsion features in spacetime theories and gravity. The Einstein–Cartan theory extends general relativity by allowing torsion to couple to spin, introducing additional geometric structure beyond curvature. Teleparallel gravity describes gravity using torsion instead of curvature. Torsion concepts also arise in the study of continuum mechanics and the deformation of materials.

In engineering and materials science, torsion describes twisting loads on objects. Torsional stiffness, polar moment of inertia, and shear stress under torque are key ideas. For a circular shaft, the shear stress at radius r is often expressed as τ(r) = T r / J, illustrating the practical role of torsion in design and analysis.

In chemistry and biochemistry, torsion relates to dihedral angles that describe rotations around bonds. Dihedral or torsion angles define molecular conformation, with implications for protein structure through backbone angles such as phi and psi.

See also torsion (disambiguation), torsion tensor, dihedral angle, and angular momentum in related contexts.