To create artificial gravity, the space station shown in thedrawing is rotating

Question

To create artificial gravity, the space station shown in thedrawing is rotating at a rate of 1.30 rpm. The radii of thecylindrically shaped chambers have the ratiorA/rB = 6.00. Each chamberA simulates an acceleration due to gravity of 8.70 m/s2.Find values for (a) rA,(b) rB, and(c) the acceleration due to gravity that issimulated in chamber B. I was able to get "C" which is 1.45 m/s^2, however, i keepgetting the other two wrong. Any help is greatlyappreciated! To create artificial gravity, the space station shown in thedrawing is rotating at a rate of 1.30 rpm. The radii of thecylindrically shaped chambers have the ratiorA/rB = 6.00. Each chamberA simulates an acceleration due to gravity of 8.70 m/s2.Find values for (a) rA,(b) rB, and(c) the acceleration due to gravity that issimulated in chamber B. I was able to get "C" which is 1.45 m/s^2, however, i keepgetting the other two wrong. Any help is greatlyappreciated!

Explanation / Answer

   we use the equation for vcentripetal accelerationas    a = v2 / r (a)    the centripetal acceleration of a point on therim of chamber A is the artificial acceleration dueto gravity givenby    aA = vA2 /rA         = 8.70 m/ s2    any point on the rim moves with a speedvA = 2 rA / T    where T is the period oftime        solve for rA    rA = ...... m   (b)    rB = rA / 6.00        = ......... m (c)    aB = vB2 /rB    vB = 2 rB/ T    aB = ........ m / s2

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