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One simple way to measure the moment of inertia of an irregular object is shown in...

One simple way to measure the moment of inertia of an irregular object is shown in the diagram. The object is mounted on a frictionless axis. A light string is wrapped around the object, passes over a light pulley (so it has negligible moment of inertia itself), and then connected to mass M = 40.6 kg. The system is released from rest. After mass M has fallen distance 4.05 m it is moving 2.67 m/s and the object has reached angular speed ω = 9.56 rad/s. Find the moment of inertia of the object, in kg-m2

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