 Solution

In cylindrical coordinates,The screw transformationleaves $r$ and $\varphi -kz$ fixed, so it is the helical symmetry of a potential. Its infinitesimal generator has ${\xi }_z=1$ and ${\xi }_{\varphi }=k$. Noether's theorem therefore gives the conserved quantityThis is a linear combination of axial linear momentum and axial angular momentum.