I remember my introductory lecture when I went to university. pretty much one of the firt things they said, was that all the physics up to that point was a load of rubbish, and would have to be relearned. Hopefully your university will pick by aptitude and ability, if so, you shouldn't have a...
note also that all the atoms that make up the structure of the tower are held together as a result of electromagnetic interactions between the atoms. This means the maximum speed of interaction between adjacent atoms is c, so the top end of the tower would just get ripped off.