A homogeneous steel wheel of radius R and mass M rolls without slipping on a horizontal rail, as shown in the Figure. A point mass m=2M is soldered at a point A of the wheel located at a distance R/2 from the center O. Assume that all the quantities mentioned so far are known, and let o be the clockwise-growing angle formed by the segment OA with the vertical direction. Find, as functions of y and p: a) The vector velocity of O. b) The vector velocity of A. c) The mechanical energy of the system. d) The equation of motion of the system

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