I've had wheel bearings do that same thing. Roar when loaded, quiet when unloaded, may just be the left one.

 

I've been trying to track down similiar issues in mine...

1. Truck Off, lift front tires and spin, the shafts spin.
2. Truck Running, lift front tires and spin, the shafts spin.
3. Shifted running truck into 4high, then back into 2wd, spun front tires, shafts did NOT spin.

Being stationary might have something to do with this test, not sure.

My most noticeable problems are vibration/grinding sound when coming to a stop. Did the brakes with no effect on the issue at all. Perhaps bearing is shot from bad iwe and grinds under braking load?

Also started testing shifting into 4high as I'm driving down my gravel drive every morning then back into 2wd, after just two days it might have improved some...not sure.

 

What year and trim level is your truck?

 

2015, Lariat

 

Not sure on the '15 & '16, but '17 up, when initial start with temps around 32F, the IWEs lock in for about a mile to warm up front diff. That could be the reason why the shafts turned with truck running in 2H. It will continue to do this if temps remain around 35F, on every start. Again, NOT sure if '15 &'16 have the warm up cycle.
Try running truck in 4A and see if noise goes away. You won't hurt anything in 4A even on dry pavement.

 

Taking my truck to another dealer tonight. Hopefully I'll know more by Wednesday. Stay tuned!

 

Keeping an eye out.

 

A better way to test to see if the half shafts turn and it can be done without lifting the truck. Try turning the half shafts by hand. Both sides in 2H should turn. In 4H, you shouldn’t be able to turn either one by hand. This will eliminate and turn the wheel may provide.

 

Although not on an F150 I had one that would come and go on a Focus. Took me a year to figure out it was a bearing when it finally started roaring on a regular basis. Whenever it did it I always thought bearing but, when it went away I’d be scratching my head as I’ve never had a bad bearing do that before.

 

call from dealer. yea we tried road testing the truck alot we hear and fell nothing abnormal. Mind you it did it the whole way to the dealer this morning.