Using electromagnets, a small-scale LED flashlight similar to that featured in "Shake It Like a Tic-Tac!" can be produced.
With the setup for the Tic-Tac flashlight, the voltage produced by the magnet alone may not be enough to power up the LED. It is possible that the only reason the LED lit up was due to the rechargable battery not being completely empty in the first place. This theoretical experiment attempts to improve on the circuit based on one of the comments made on "Shake it like a Tic-Tac!"
Image taken from Shake it like a Tic-Tac! page