A stationary platform which can rotate freely about a vertical axis (Fig. 1.72) 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 ωo about a shaft BB' coinciding with the axis OO'. The moment of inertia of the sphere relative to the rotation axis is equal to Io. 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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B- Fig. 1.72.