A large horizontal circular platform $($M$=101$ kg$,$ r$=4\mathrm{.}63$ m$)$ rotates about a frictionless vertical axle. A student $($m$=76\mathrm{.}91$ kg$)$ walks slowly from the rim of the platform toward the center. The angular velocity of the system is $3\mathrm{.}66$ rad$/$s when the student is at the rim.

Find the moment of inertia of platform through the center with respect to the z$-$axis.

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Find the moment of inertia of the student about the center axis $($while standing at the rim$)$ of the platform.

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Find the moment of inertia of the student about the center axis while the student is standing $1\mathrm{.}36$ m from the center of the platform.

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Find the angular speed when the student is $1\mathrm{.}36$ m from the center of the platform.