Quote:
You seemed to be saying on the one hand that the plane was moving relative to the ground


YES !! the top of the plane is relatively moving faster than the ground.

you dont have to use the center of an object you can use any point of the object when calculating the angular velocity
of a point on the object relative to any other point on the object.

aircraft use two ways of measuring speed.

air speed and ground speed.

air speed is the measurement of the aircraft speed.
ground speed represents the actual displacement of the aircraft at ground level.

air speed is always greater than ground speed.


Quote:
and on the other, that the balloon was not moving relative to the ground. Can both be true?


absolutely !!

http://en.wikipedia.org/wiki/Motion_(physics)

consider a record on a turntable , the outer edge of the record
will have a greater angular velocity than the center of the record.

so relative to the grooves of the second song on the record the grooves of the first song on the record will always have a
greater angular velocity , when the record player is turning
the record that is.






3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.