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Bent shaft ABC is welded to the vertical shaft, which rotates at constant speed Ω. The angle of rotation of the square plate about axis BC is φ, which is an arbitrary function of time. The configuration depicted in the sketch, in which the plate is situated in the vertical plane, corresponds to φ = 0. The xyz coordinate system is attached to the plate. (a) Derive expressions for the angular velocity and angular acceleration of the plate, valid for arbitrary φ, in terms of components with respect to xyz.
(b) Derive expressions for the velocity and acceleration of the center of the plate in terms of xyz components.
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