In designing rotating space stations to provide forartificial-gravity environmen

Question

In designing rotating space stations to provide forartificial-gravity environments, one of the constraints that mustbe considered is motion sickness. Studies have shown that thenegative effects of motion sickness begin to appear when therotational motion is faster than approximately 2.25 revolutions per minute. On the other hand,the magnitude of the centripetal acceleration at the astronauts'feet should equal the magnitude of the acceleration due to gravityon earth. Thus, to eliminate the difficulties with motion sickness,designers must choose the distance between the astronaut's feet andthe axis about which the space station rotates to be greater than acertain minimum value. What is this minimum value?
1 m

Explanation / Answer

There are two formulas for figuring the acceleration of somethinggoing in a circle. One formula uses linear speed (v); the otheruses angular speed (). Since they are talking about"revolutions per minute", they're talking about angular speed, souse that formula here. acceleration = ²r Now, they want the acceleration to match earth's gravity, "g". So,they want this: g = ²r Now, they also said they want the angular speed to be less than orequal to 2.25 revolutions per minute: = (2.25(2 rad)/min)² / g Also, it's good to use "seconds" instead of "minutes", since g willprobably have "seconds" in it too: r >= (2.25(2 rad)/(60sec))² / g Now just use your calculator.

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