A few notes on the puzzle:
1. A half-full container of honey does pretty well in reproducing the behaviour of the mystery cylinder. I wonder if the motion is a little smoother or more periodic with the ping-pong balls because they move as organized objects - also the delays between motion seemed to be longer with them than without ping pong balls.
2. For the average speed track problem, every time I said velocity I meant speed. Sorry to the pedants out there who are perhaps looking for some trick answer due to displacement being zero when you run around a track.
3. Although a lot of people identified it was something about a train's wheels that move backwards, fewer identified that specifically it was the part of the flange below the rail. Some simply said the bottom half of the wheel.
4. The bicycle question is perhaps the most complex of these riddles. If you tried it with a bike you likely found that it went backwards. But what happens if you sit on the bike and only push backwards on the bottom pedal. The answer might surprise you so give it a shot!