Question

It is proposed that future space stations create an artificial gravity by rotating. Suppose a space station is constructed as a 800-m-diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. What rotation period will provide "normal" gravity?

Answer 1

Answer:

T=56.77s

Explanation:

We must use the formula for centripetal acceleration:

$a_{cp}=\frac{v^2}{r}$

We know the radius r and we want is to obtain a centripetal acceleration equal to g. Since velocity is distance over time, on this circle we can take distance as the circumference (which is of value $2\pi r$) and thus the time will be the period T because that's the time a point takes to travel the whole circumference, so we can write:

$g=a_{cp}=\frac{v^2}{r}=\frac{(\frac{2\pi r}{T})^2}{r}$

or:

$g=\frac{4\pi^2 r}{T^2}$

and since we want the period:

$T=\sqrt{\frac{4\pi^2 r}{g}}=2\pi\sqrt{\frac{r}{g}}$

which for our values is:

$T=2\pi\sqrt{\frac{(800m)}{(9.8m/s^2)}}=56.77s$