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A helical symmetry combines an axial rotation and a proportional axial translation. A helix with $z=b\theta$ is unchanged as a set by this transformation. If a mechanical Lagrangian is invariant, the Noether conserved quantity for a mechanical point symmetry is $L_z+b{P}_z$, where the two momenta include all moving components. Pure axial rotation and pure axial translation need not separately be symmetries. The helical symmetry of a potential is a related special case in which the constraint is replaced by an invariant potential.^[ref]

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.