Rigidity or shear modulus

The stress = tangential force (F)/ area over which applied (A)
The strain = angle of shear = x/y - for small angles.
Therefore:

For a wire the restoring torque (T) when twisted through an angle q is


where c is a constant.

This means that a wire will twist by a large amount for a given torque if its modulus of rigidity is small. The ability to resist or allow twisting is of vital importance in the design of buildings and in the materials used for drive shafts in engines and suspensions in meters. Clearly a drive shaft with low rigidity would be useless, as would a meter suspension with a very high rigidity.

If a spiral spring is stretched all parts of the spring will become twisted. The extension of the spring therefore depends on both its modulus of rigidity and size.