After a short interval of speeding up from rest, the ride spins at a constant rate about its central axis. Passengers may choose to sit in either an inner seat, located a distance R from the axis, or an outer seat, at a distance 1.7R from the axis. The seats are held in place by very strong, rigid metal bars. Bernice is a bit nervous about going on this ride, because she tends to get motion sickness. However, she agrees to go with Gertrude as long as she can choose a seat with the smallest possible magnitude of acceleration, which should give the most comfortable ride. They are having a discussion about whether the inner seats or the outer seats will be better for this purpose. Bernice: "The radial acceleration is equal to v2/r, so it’s inversely proportional to r. The outer seat is at a larger radius, so it should have less acceleration."Gertrude: "But the radial acceleration is also equal to ω2r, which is directly proportional to r. That would mean the inner seat, at a smaller radius, should have less acceleration."a) Whose argument is correct? Which seat actually has less radial acceleration? What is wrong with the argument that is incorrect? Explain your reasoning.
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