A) You\'re out in space, on a rotating wheel-shaped space station of radius 1384

Question

A) You're out in space, on a rotating wheel-shaped space station of radius 1384m. You feel planted firmly on the "floor", due to artificial gravity. The gravity you experience is earth- normal, that is, g=9.8 m/s^2. How fast is the space station rotating in order to produce this much artificial gravity? (answer in revolutions per minute (rpm))

B) What would the radius of the space station have to be, rotating at the rate you calculated in part (A), to produce artificial gravity of 30 m/s^2? (answer in m)

Explanation / Answer

given

R = 1384 m

g = 9.8 m/s^2

let w is the required angular speed of the wheel

A) Apply, a_rad = R*w^2

g = R*w^2

==> w = sqrt(g/R)

= sqrt(9.8/1384)

= 0.084 rad/s

= 0.084*(60/(2*pi)) rev/min

= 0.802 rpm

B) Again Apply, a_rad = R*w^2

g = R*w^2

==> R = g/w^2

= 30/0.084^2

= 4252 m

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