Torzió

Torzió, commonly translated as torsion, is the twisting of an object caused by an applied torque. It describes an angular displacement around the object's axis and is a central concept in mechanics, structural engineering, and mathematics. In everyday devices, torsion is exploited in shafts, gears, and torsion springs, which store energy by twisting.

In solid mechanics, torsion analysis often concerns circular shafts. For a shaft of radius R subjected to torque T, the shear stress at the outer surface is tau = T R / J, where J = π R^4 / 2 is the polar moment of inertia. The maximum shear stress is tau_max = 2T / (π R^3). The angle of twist per unit length is given by theta/L = T / (G J), with G the shear modulus. Non-circular cross-sections require consideration of warping, described by Saint-Venant torsion. Torsion springs rely on this principle to provide rotational resistance and energy storage.

In mathematics, torsion of a space curve measures how the curve departs from planarity. For a smooth curve r(s) parameterized by arc length, torsion τ quantifies the rotation rate of the curve’s osculating plane and can be computed as τ = (r' × r'') · r''' / |r' × r''|^2. Planar curves have zero torsion.

In abstract algebra, torsion refers to elements of finite order in a group or module. The torsion substructure consists of all elements of finite order. The term also appears in related areas of topology and differential geometry, where torsion concepts help describe invariants and properties of geometric objects.