Brushbots and Kapitza's pendulum
A brushbot is what you get if you tape a cell phone motor to the back of a toothbrush head. When you turn on the motor and put it down on its bristles, it skitters across the floor and is great fun. I'll talk about some of the math behind why a brushbot doesn't just tip over, even if you use a new toothbrush in which the bristles are pointed inwards so it isn't stable standing on its bristles. Of course, there will be brushbots for everyone to play with.