  Although progress has been made recently in defining nontrivial uncertainty
limits for the SU(2) group, a description of the intermediate states bound by
these limits remains lacking. In this paper we enumerate possible uncertainty
relations for the SU(2) group that involve all three observables and that are,
moreover, invariant under SU(2) transformations. We demonstrate that these
relations however, even taken as a group, do not provide sharp, saturable
bounds. To find sharp bounds, we systematically calculate the variance of the
SU(2) operators for all pure states belonging to the $N=2$ and $N=3$
polarisation excitation manifold (corresponding to spin 1 and spin 3/2).
Lastly, and perhaps counter to expectation, we note that even pure states can
reach the maximum uncertainty limit.
