Astronauts who spend a long time in space experience a loss of bone density due

Question

Astronauts who spend a long time in space experience a loss of bone density due to the lack of gravitational acceleration. Therefore, it would be helful to have articial gravity on a space station. One way to accomplish this is to spin the station about its central axis. a If a space station orbitiong the moon has a radius of 50.0m with what anglar speed must the station be rotationg to give the astronaunts an apparent weight 3/4 of their weight on the earths surface at the outer edge. b what is the apparent weight of a 65.0kg astronaut halfway from the center to the edge of the station

Explanation / Answer

so

g = centrip acc

9.80*3/4 = w^2 r

7.35 = w^2 * 50.0

w = 0.3834 rad/s is the angular speed

since acc is prop to r, at half the radius he would feel half times 3/4 his weight or

1/2 * 3/4 * 9.80 * 65.0 = 239 N is his apparent weight

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