This is a really quick but sort of amusing demo about angular momentum.
Set down each egg at rest on the tray. One by one, flick the egde to get them spinning. Have the students guess which one is boiled and which one is raw. If you want to make it interesting, have a student agree to try to catch the one that he/she things is boiled. This can get messy if the guess is wrong.
The boiled egg is a rigid body and will spin smoothly at a nearly constant angular velocity. The raw egg will gradually transfer angluar momentum from the shell to the yolk, so the rotation of the shell will slow.
A more dramatic demonstation is to momentarily stop a rotating egg by putting your finger on the shell, then releasing it. The hard boiled egg will simply stop and stay stopped, but the raw egg will start rotating again as the yolk transfers angular momentum back to the shell.