  The disputed question of uncertainty relations (UR) on a circle is regarded
as a particular element of a more general problem which refers to the quantum
description of angular observables $L_z$ and $\phi$. The improvised $L_z-\phi$
UR are found to be affected by unsourmontable shortcomings. Also in
contradiction with a largely accepted belief it is proved that the usual
procedures of quantum mechanics are accurately applicable for the $L_z-\phi$
pair. The applicability regards both the known circular motions and the less
known non-circular rotational motions. The presented facts contribute as
arguments to the following indubitable conclusions: (i) the traditional
interpretation of UR must be denied as an incorrect doctrine, (ii) for a
natural physical consideration of the the $L_z-\phi$ pair the results from the
usual quantum mechanics are sufficient while the improvised $L_z-\phi$ UR must
be rejected as senseless formulas and (iii) the descriptions of quantum
measurements have to be done in a framework which is distinct and additional in
respect with the usual quantum mechanics.
