The earth spins at a (fairly) constant rate, the further away an attached object is from earth, the faster it moves. Therefore, it has a velocity relative to earth, allowing it to enter orbit through centripetal force.
That's my understanding anyway
The mass on the tower on the equator would have a higher velocity than earth's rotation, allowing it to stay up and orbit. The mass on the tower of the north pole has no velocity relative to earth though
Did people put the object dropped from the tower at the equator will orbit the earth, and stay motionless relative to the tower? I've spoken to 30ish people about it, everyone had something different :(