How about an apparent perpetual motion device? Apparent meaning that most people will think that it's impossible and that the videos are Youtube frauds, quite likely your physics teacher as well!
It's called Directly Downwind Faster Than The Wind or DDWFTTW for short. This topic has been hotly discussed on many internet forums over the last four years (including here) and has just recently been proven with a full scale vehicle, setting a land speed record in a new category made specifically for it. A small model can be built for less than $100 and be demonstrated working in the classroom or at a science fair using a typical treadmill.
Here's an early video of a small scale test:
http://www.youtube.com/watch?v=aJpdWHFqHm0&feature=related
Here's a very good explanation of the mechanics behind it:
http://www.youtube.com/watch?v=k-trDF8Yldc&feature=related
Here's how to build a small model that you can run on a treadmill (scroll down to find the picture of the plans and click on the picture - can't seem to link it directly):
http://www.rtfa.net/tag/cart
With videos taking you through the build:
http://www.youtube.com/watch?v=T-ArigMKhi4&fmt=18
http://www.youtube.com/watch?v=p0rhgop5wEM&feature=related
http://www.youtube.com/watch?v=gSHNqrF93MU&feature=related
Here's a video showing the model in action on a treadmill (the test shown was to disprove some deniers' claims about the vehicle):
Here's Mac Gaunaa demonstrating the model to a group of world class aero physicists(!):
http://www.youtube.com/watch?v=MLFb1-GoqNY&feature=related
With the first of his six part explanation of wind powered carts:
http://www.youtube.com/watch?v=4ZjX_DIosM8&feature=related
And finally a video that you can have playing in the background, showing a recent test of a full-sized, manned vehicle that goes faster than the wind powering it:
http://www.youtube.com/watch?v=5CcgmpBGSCI&feature=related
This concept can be as simple or as complex as you have time for. You demonstrate the idea behind it with a Yo-Yo and then back it up with the math. Another group of high school students used this for their science fair and won first prize with it.
If you can understand all the important parts of what makes this simple looking device work, you'll have a big head-start on a college level physics course. Cheap and easy to build, demonstrates a wide range of physics, controversial, and a proven winner!