From googling, I suspect this is a particular form of rotor used to wind the mainspring of an automatic watch. In this case, 'Schwung' probably combines the concepts of motion and momentum.

For a nice illustration (in English), see:

Above is a bumper automatic movement. The sickle-shaped weight stamped "Military" is the rotor. It moves back and forth, and is connected centrally to a sort of axle. By moving back and forth, it winds the mainspring. To the right, you can see one of the fixed springs which cushion the rotor as it comes around. This can cause a tactile sensation to the wearer, as the rotor smacks into spring. I really like the bumper auto.
http://alanwatch.homestead.com/bumper.html

Sample reference for Schwungrotor:

Uhrenlexikon5
Kompakter Schwungrotor einer Automatikuhr, der durch seinen kleineren Durchmesser in das Uhrwerk integriert werden kann und dadurch die Gehäusehöhe voll ...
www.onlinewatches.de/wichtige_infos5/ AGB5/Uhrenlexikon5/uhrenlexikon5.html