A sleeping area for a long space voyage consists of two cabin each connected by a cable to a central hub as shown http://www.webassign.net/sercp8/p7-26.gif. The cabins are set spinning around the hub axis, which is connected to the rest of the spacecraft to generate artificial gravity in the cabins. A space traveler lies in a bed parallel to the outer wall as shown in the figure.
a.) with r=10.0 m, what would be the angular speed of the 60.0-kg traveler need to be if he is to experience half his normal Earth weight?
b.) If the astronaut stands up perpendicular to the bed, without holding on to anything with his hands, will his head be moving at a faster, a slower, or the same tangential speed as his feet? Why?
c.) Why is the action in part (b) dangerous?

Question

A sleeping area for a long space voyage consists of two cabin each connected by a cable to a central hub as shown http://www.webassign.net/sercp8/p7-26.gif. The cabins are set spinning around the hub axis, which is connected to the rest of the spacecraft to generate artificial gravity in the cabins. A space traveler lies in a bed parallel to the outer wall as shown in the figure.  
a.) with r=10.0 m, what would be the angular speed of the 60.0-kg traveler need to be if he is to experience half his normal Earth weight?
b.) If the astronaut stands up perpendicular to the bed, without holding on to anything with his hands, will his head be moving at a faster, a slower, or the same tangential speed as his feet? Why?
c.) Why is the action in part (b) dangerous?

anonymous · Answer

page not found, but i'm suspecting it having something to do with centripetal force.
for a)
$F_g /2=F_C$, so  $mg=m\frac{v^2}{r}$
$g/2=\frac{(r \omega )^2}{r}$，as you can see the weight of object is unrelated.
$g/2=r \omega^2$
sub g=9.8, r=10 to get omega.

b) $v=r \omega$, since omega is constant (the angle subtended is the same on the same line.) so v and r is directly proportional wrt each other.

c) blood will rush to the feet because of centripetal force.