Answer
People should feel an effect of 0.90 g when the station rotates at a rate of 1700 rev/day.
Work Step by Step
$\frac{v^2}{r} = a$
$v^2 = ar$
$v = \sqrt{ar}$
$v = \sqrt{(0.90)(9.8 ~m/s^2)(550 ~m)}$
$v = 69.65 ~m/s$
We can use the velocity to find the number of revolutions per second. Let $z$ be the number of revolutions each second. So,
$z\times 2\pi r = v$
$z = \frac{v}{2 \pi r}$
$z =\frac{69.65 ~m/s}{(2)(\pi)(550 ~m)}$
$z = 0.020 ~rev/s$
We can convert the rate of rotation to revolutions per day:
$z = (0.020 ~rev/s)(\frac{24\times 3600 ~s}{1 ~day})$
$z = 1700 ~rev/day$
People should feel an effect of 0.90 g when the station rotates at a rate of 1700 rev/day.
