Spin them!

The raw eggs are still a viscous liquid inside, so they will not spin as well. The liquid will rotate chaotically inside the egg, hitting against shell and causing energy loss, leading to shorter spin times. The inside of the boiled eggs is hard and will rotate alongside the shell without a hitch.

Alternatively, after spinning the eggs, bring them to a hard stop and immediately release them. The raw egg will start wobbling noticeably because the liquid inside is still spinning and hitting the shell due to inertia.