a person in a workshop invents an antigravity device, on switching it on would this device immediately fly into the top of the western wall at the speed of the earths rotation at its surface as this device would no longer be part of the earths gravitational system?
Gravity is not of the earth as such its a force created by the mass of an object in the fabric of space time so if you eliminated earths gravity it would be attracted to the next strongest force actng upon it proberbly the sun. But if your invention was to counteract all gravity then I suspect the object would sit motionless.
Relative to the floor it wouldn't move. It would still have its horizontal component of velocity but would have zero weight unless this hypothetical device produced a repulsive force upwards?