When an object rotates around an axis on a curved surface, it will not rotate 90 degrees.

In mathematics and geometry, when an object rotates around an axis, every point of the object will rotate around the axis, but the rotation angle is not necessarily 90 degrees. The rotation angle depends on the selected axial and rotation operation.

If you rotate the plane shape around the axis, rotating it by 90 degrees will make the plane shape completely perpendicular to the original position.