If the loop rotates about `Z` axis, the variation of flux linkage will be zero. Therefore no emf is induced. Consequently no current flows in the loop
When it rotates about `y`-axis, its flux linkage changes. However, in insulators there can not be motional emf.
If the loop is made of copper, it is conductive therefore induced current is set up.
If the loop moves along the `Z` axis variation of flux linkage is zero. Threfore the emf and current will be equal to zero.