ask the library to digitize either my copy or theirs for showing in class?
There is nothing in section 110(1) that addresses “reproduction” which is what migrating your VHS copy to digital format would be. In order for you, the professor, to digitize your VHS, you would have to rely on fair use (see question #5, below), which may justify digitizing portions of the work, but probably not the entire movie. If the work is available in digital format, buy it (or ask your library to buy it) and you can show that. If the work is not available in digital format for you or your library to purchase, your library can digitize its VHS copy as long as it can be reasonably described as deteriorating. The library is allowed to do this pursuant to a different section of the Copyright Act.