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An astronaut (mass m), somewhere out in space, far from gravitating objects, is wearing magnetic boots and is standing at the center of a thin metal disc of mass M and radius R. The disc rotates about the ê2 axis (lying in the plane of the disc and going through its center) with angular speed wo, as depicted in the Figure. (Assume m < M, so that you may ignore any effects of the astronaut's presence on the inertia tensor of the disc.) (a) (12 points) At t = 0, the astronaut begins to walk at constant speed v along the positive ê₁ axis. Find the net fictitious force which the astronaut feels in the rotating orthogonal frame of reference (ê1, 2, 3)? Express your answer in terms of m, v, wo, time t, and the three orthogonal base unit vectors ê₁, 2, and ê3, oriented so that ê₁ and ê2 lie in the disc plane and ê3 is perpendicular to the disc plane. (b) (8 points) The magnetic boots have a limit |Fmax| on the amount of force they can provide to counteract ♬ and keep the astronaut moving at constant speed. Find the maximum speed v at which the astronaut can walk, in terms of Fmax, m, wo, v, and t. ^>