Just recently I've started hearing a whirring noise when I turn either left or right. Doesn't matter if the tires are turning or not. Any ideas?

 

06 f150

 

One possibility is the power steering pump. Check the power steering fluid level and then for leaks. If you can't find anything but the noise remains, I highly recommend you take it to a shop that can check it out for you. Some shops do this for no or little cost. I've been on the road when a power steering pump finally fails and it's no fun. Captian America would have a hard time turning the wheels of our big trucks without power steering. Just a recommendation though. Good luck.

 

If you're up around hundred k or more miles, your serpentine belt pulley bearings are well past their prime. Check your idler pulley bearings for wear that would cause them to whine when under load, check you belt condition well you're at it.