So you want to rotate the core?
If that's what I understand it will be a first. But again I believe it'll have no effect. Your transformer has two sides, a primary and secondary. As the current starts to flow in the primary, say from zero to I-max, a magnetic field is induced in that conductor, and this field cuts the secondary conductor, producing a current in it, although no physical connection exist between secondary and primary.
Remember, a current will still be induced in the secondary conductor, even if no steel core is used, it referred to as air core.
The function of the steel core is to intensify the flux. Spinning it will probably have no benefit, except to cut your coils.
So, at any point that only a static current flows through the primary coil, nothing will happen in the secondary coil, like 0V reading will be taken. It has to change, magnetic flux has to cut the conductor to induce current flow.
Hope it helps