This reminds me of a story about, IIRC, Soviet intelligence personnel determining that a photocopy machine at their consulate in the USA was bugged by the CIA by measuring it's weight and comparing that value to the standard value published by Xerox.
is measuring the moment of inertia not standard? I think any mechanical engineer would suggest it for that kind of problem (disclaimer; I've suggested it before for the same problem)
Modern times, but same old methods of "debugging"
The angular momentum stuff is innovative though.