can you help me understand this step-by-step: In designing rotating space statio

Question

can you help me understand this step-by-step:

In designing rotating space stations to provide for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the negative effects of motion sickness begin to appear when the rotational motion is faster than two 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 gravity on earth. Thus, to eliminate the difficulties with motion sickness, designers must choose the distance between the astronauts' feet and the axis about which the space station rotates to be greater than a certain minimum value. What is this minimum value?

Explanation / Answer

from the given data,

the maximum angular speed, w = 2 rev/min

= 2*2*pi/60

= 0.2094 rad/s

let r is the distance between the centre to austonait feet.

we know, centripetal accelerattion = r*w^2

g = r_min*wmax^2

r_min = g/w_max^2

= 9.8/0.2094^2

= 223.5 m

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