What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?

The total moment of inertia of the system is the sum of the moment of inertia of the disk plus the moment of the inertia of the person.

The moment of inertia of a uniform disk is Id = [1/2] Md * (R^2)

And the moment of inertia of the person standing on the rim of the disk is Ip = Mp(R^2).

So the total amounf ot inertia is: I = Id + Ip = [1/2]Md(R^2) + Mp(R^2).

There you only need to plug in the values that you are given for the problem:

 If Md = 193 kg, Mp = 77 kg, and R = 2.07 m

I = [1/2]*193kg*(2.07m)^2 + 77kg * (2.07m)^2 = 743.43 kg * m^2

743.43 kg * m^2

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