The Ferris wheel at an amusement park has an even number n of gondolas, each freely pivoted at its point of support on the wheel periphery. Each gondola has a loaded mass m, a radius of gyration k about its point of support A, and a mass center a distance h from A. The wheel structure has a moment of inertia I_O about its bearing at O. Determine an expression for the tangential force F which must be transmitted to the wheel periphery at C in order to give the wheel an initial angular acceleration a starting from rest. Suggestion: Analyze the gondolas in pairs A and B. Be careful not to assume that the initial angular acceleration of the gondolas is the same as that of the wheel. (Note: An American engineer named George Washington Gale Ferris, Jr., created a giant amusement-wheel ride for the World’s Columbian Exposition in Chicago in 1893. The wheel was 250 ft in diameter with 36 gondolas, each of which carried up to 60 passengers. Fully loaded, the wheel and gondolas had a mass of 1200 tons. The ride was powered by a 1000-hp steam engine.)

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A A R B.