I should be able to answer this, but I'm clearly missing something. It
may be in my visualization, it may be in my interpretation, or I may
just be dense. Regardless, I throw myself upon your mercies:
A classic application of conservation of angular momentum, often cited
in physics texts, is the joining of two cylinders rotating about a
common axis. When the cylinders are allowed to meet "face-on", the
angular momentum of the system is conserved. When cylinders rotating
about parallel axes meet "edge-on", however, the angular momentum of the
system may not be conserved.
In the latter case, imagine two cylinders, one initially rotating and
the other stationary. If they are gently brought into contact,
frictional force between the cylinders acts to slow the original
cylinder's rotation and induce rotation in the other cylinder. HRW
(fifth edition), chapter 12, question 49, is an example of this
situation, and in the problem the authors claim that angular momentum is
not conserved. If they mean that the angular momentum of the system is
not conserved, I do not see the source of the external torque (unless
the frictional force is responsible, though it would seem to be internal
to the system as it acts only between the cylinders).
The former case is also discussed in HRW5, chapter 12, question 53; the
coupling of the cylinders "face-on" is said to maintain angular momentum
(though friction between the cylinders seems to be responsible for their
eventual rotation as a unit).
Why are the two situations different in how conservation of angular
momentum is applied? I seem to be missing something which I feel is
very important.