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A stationary platform P which can rotate...

A stationary platform P which can rotate freely about a vertical axis (figure) supports a motor M and a balance weight N. The moment of inertia of the platform with the motor and the balance weight relative to this axis is equal to I. A light frame is fixed to the motor's shaft with a uniform sphere A rotating freely with an angular velocity `omega_0` about a shaft `BB^'` coinciding with the axis `OO^'`. The moment of inertia of the sphere relative to the rotation axis is equal to `I_0`. Find
(a) the work performed by the motor in turning the shaft `BB^'` through `90^@`, through `180^@`,
(b) the moment of external forces which maintains the axis of the arrangement in the vertical position after the motor turns the shaft `BB^'` through `90^@`.

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