Well I see my icon rotating during boot and when I launch any application and when I send email; so it is obviously scanning files, emails, etc. and the icon rotates.
Stopping one shield other than the file system shield shouldn't impact on the others. However, when you stop a shield you get the yellow triangle and exclamation mark over the avast icon, so that status won't be animated.
If you change the avastUI, Settings, Status Bar and uncheck the monitoring of the shield you have stopped, no exclamation mark and the icon rotates again.