  We discuss the uncertainty relation for the azimuthal angle $\phi$ and the
$z$-component of the angular momentum $L_z$. To this end we derive the
uncertainty relation for an arbitrary pair of observables and discuss the
conditions for its validity. By means of a simple parameter-dependent state we
illustrate the well known fact that the standard uncertainty relation for the
coordinate and its conjugate momentum does not apply the pair of observables
$\phi-L_z$. This analysis is motivated by a discussion of the motion of an
electron in a constant magnetic field appeared recently in this journal (Eur.
J. Phys. \textbf{33} (2012) 1147) where the author assumed the validity of the
standard uncertainty relation for the pair $\phi-L_z$.
