Maybe a POV display?
Physics students will get the concept of POV, and from a programming standpoint, it brings Bitmapped graphics (fonts), bit shifting, binary in general.. as well as timing and interrupts (use an interrupt with a hall sensor or phototransistor for rotation speed sensing).
An 8-bit POV direct driven (arduino can power 8 normal LEDs @20ma fairly easily), mount it on a disc of some type and then counterbalance. If you get the balance decent, a small DC motor will drive it. Some folks do this with a "propeller" design, but it's easier to build and balance if a disc of some type is used, imo...
For extra credit, accept input to the POV via IR Remote.. update the text (and store to EEPROM) without a computer...
Still a VERY do-able project that covers MANY concepts..
It also involves objects being rotated at speeds which approach the dangerous and destructive if items are not attached extrenely well. Physics students always appreciate a 9v battery embedded in the ceiling (or the cat, their own face, etc) because they thought tape would hold up to being spun at 2000RPM. Now I'm a big believer in Duct Tape mind you... but have your students calculate the kinetic energy of a 9v battery being rotated at few hundred (or thousand!) RPM on an 18" (.5 meter) radius. Then ask them if they want to stand in the trajectory path, just using Duct Tape.
I have a nice dent in the plasterboard to attest to Duct Tape not being good enough for THIS particular function... though it has given me an idea for a high-speed Fully Automatic Trebuchet..
My town has some strange laws on it's books.. not the least of which makes "The construction and/or ownership of an (get this!) Infernal Device" a crime. I consider it a good thing to violate this law as often as possible.
We also are the only city in the USA with an ordinance prohibiting the use of Atomic Weapons within the city limits. You really don't want to mess with the local cops. It's the fear of retribution from our local police force which held the Russkies in check, you know...