Sorry, this is completely OT, but since you asked: "If toast
  always lands butter-side down, and cats always land on their feet, what
  happens if you strap toast on the back of a cat and drop it?"

The answer is you get both perpetual motion and anti-gravity. The problem is that one cat is not enough. The trick is to multiplex cats into cat-toast arrays. Get about 50 in synch and you can run a small turbine. The other problem is feeding them while they spin, because they lose the feet-landing ability if they expire.