Gyroscope in a suitcase
Gyroscopes are strange enough when you can see that they are spinning, but if you can't they are truely bizzare. This consists of a suitcase with a large gyroscope built in.
This was built as a show demo and has an integral motor and battery, so it will spin itself up.
This is a powerful counterintuitive demonstration of the effects of angular momentum, it will sit at an angle on a rotating platform, lift up when you go around a corner, or apparently spontaneously start spinning when you switch off the motor.