Mission: Space is a ride at EPCOT that simulates a mission to Mars. While nowhere near...

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Mission: Space is a ride at EPCOT that simulates a mission to Mars. While nowhere near as good as the ride it replaced, it is still a pretty cool ride from a certain point of view. The sensation of the g-forces during a rocket launch is simulated via a centrifuge. Let point O denote the center of the centrifuge, and let point P denote a rider on the perimeter. Let R be the radius of the centrifuge, and let be the angle measuring the orientation of the centrifuge; note that neither nor its derivative is constant. Kinematically speaking, this is identical to the very first example we did in class. Therefore, you may use those results and skip directly to the kinetics to solve this problem. Ignore the Earth's actual gravity. Determine: a) the rotational speed required (in rpm) to simulate 2.5 g if R = 30 feet; b) what an astute Isaacolyte might notice while in the centrifuge that would break the immersion. That is, use your kinetics result to determine how rotating in a centrifuge is kinetically different from a rocket launch. Figure 2: Visual of the centrifugal layout of the ride pods in EPCOT's Mission: Space. (Credit to Mackenzie Peck for this idea.) Mission: Space is a ride at EPCOT that simulates a mission to Mars. While nowhere near as good as the ride it replaced, it is still a pretty cool ride from a certain point of view. The sensation of the g-forces during a rocket launch is simulated via a centrifuge. Let point O denote the center of the centrifuge, and let point P denote a rider on the perimeter. Let R be the radius of the centrifuge, and let be the angle measuring the orientation of the centrifuge; note that neither nor its derivative is constant. Kinematically speaking, this is identical to the very first example we did in class. Therefore, you may use those results and skip directly to the kinetics to solve this problem. Ignore the Earth's actual gravity. Determine: a) the rotational speed required (in rpm) to simulate 2.5 g if R = 30 feet; b) what an astute Isaacolyte might notice while in the centrifuge that would break the immersion. That is, use your kinetics result to determine how rotating in a centrifuge is kinetically different from a rocket launch. Figure 2: Visual of the centrifugal layout of the ride pods in EPCOT's Mission: Space. (Credit to Mackenzie Peck for this idea.)