  The equality in the uncertainty principle for linear momentum and position is
obtained for states which also minimize the uncertainty product. However, in
the uncertainty relation for angular momentum and angular position both sides
of the inequality are state dependent and therefore the intelligent states,
which satisfy the equality, do not necessarily give a minimum for the
uncertainty product. In this paper, we highlight the difference between
intelligent states and minimum uncertainty states by investigating a class of
intelligent states which obey the equality in the angular uncertainty relation
while having an arbitrarily large uncertainty product. To develop an
understanding for the uncertainties of angle and angular momentum for the
large-uncertainty intelligent states we compare exact solutions with analytical
approximations in two limiting cases.
