Does the Dip Angle Change on a Rollercoaster with a Rotating Compass?

[hankaaron]

Say I had a special type of compass which was free to rotate about its axis in the vertical plane. If I were to ride a roller coaster which had a 360 loop, would the dip angle of the compass needle change as I rode through the loop?

 

[CWatters]

The dip angle depends on where you are on the planet in relation to the poles. If this "dip meter"was sensitive enough I can't see why it wouldn't change. I suppose if the loop were orientated east-west at the equator the change would be smaller than if north-south elsewhere.