To me it sounds like what can happen if you disable Vertical Sync on games when there running at too fast a speed. You can enable this usually in Options in games.
If its not here, go to the video settings (right click desktop, Properties, settings tab, Advanced, and find a tab with 'Wait for Vertical Sync' and enable it there. You will find this is probably the problem.
Vertical sync is basically where the video syncs itself with the refreshing of the vertical syncing of the monitor to make a new image appear (most monitors range from 60,70) and so the video card will try its best to send out a new image at these points. If though it is disabled, the video card sends them out whenever it can, and this can be in the middle of a refresh of the monitor which is where the lines are coming from when you spin.
Most computers i'd say to disable it anyway as it doesn't bother most people, and tends to make the game feel like its running slower if its exceeding the monitors rate, though 60,70fps on a game these days is fine, and is not great for slow computers.
So enable this, and I hope the problem goes away
EDIT: It might be best to make it "default on' as some games won't work that well with it, and then this will let you change it within the game if it has the setting. Making it 'Always on' will force the graphics card to use it all the time