An interesting example of angular momentum conservation is the following experiment.
The student sits on a low-friction turn-chair with weights extended. Because of the extended weights his/her overall rotational inertia is relatively large in this position.
As he/she slowly turns, his/her angular momentum is the product of his/her rotational inertia and rotational velocity. When he/she pulls the weights inward, his/her overall rotational inertia is considerably decreased.
What is the result? His/her rotational speed increases!
This is best appreciated by the turning person who feels changes in rotational speed that seem to be mysterious. But it's straight physics!