= Solution
In <cylindrical coordinates>,
$$
L=\frac m2(\dot r^2+r^2\dot\phi^2+\dot z^2)-f(r,\phi-kz).
$$
The screw transformation
$$
z\mapsto z+s,
\qquad
\phi\mapsto\phi+ks
$$
leaves $r$ and $\phi-kz$ fixed, so it is the <helical symmetry of a potential>. Its infinitesimal generator has $\xi_z=1$ and $\xi_\phi=k$. Noether's theorem therefore gives the conserved quantity
$$
\boxed{p_z+kp_\phi
=m\dot z+kmr^2\dot\phi}.
$$
This is a linear combination of axial <linear momentum> and axial <angular momentum>.
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