Statement of a problem № 42049


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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