Why do we care about a material's ability to resist torsional deformation?

(a) because the angle of twist of a material is often used to predict its shear toughness
(b) because rotating shafts are used in engineering applications
(c) we don't care - simply an academic exercise.
(d) because it can determine g and inform us of a materials ability to resist shear deformation

(A) Because the angle of twist of a material is often used to predict its shear toughness

Explanation:

In engineering, torsion is the solicitation that occurs when a moment is applied on the longitudinal axis of a construction element or mechanical prism, such as axes or, in general, elements where one dimension predominates over the other two, although it is possible to find it in diverse situations.

The torsion is characterized geometrically because any curve parallel to the axis of the piece is no longer contained in the plane initially formed by the two curves. Instead, a curve parallel to the axis is twisted around it.

The general study of torsion is complicated because under that type of solicitation the cross section of a piece in general is characterized by two phenomena:

1- Tangential tensions appear parallel to the cross section.

2- When the previous tensions are not properly distributed, which always happens unless the section has circular symmetry, sectional warps appear that make the deformed cross sections not flat.