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tia_tia [17]
2 years ago
13

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?
Physics
1 answer:
Vesna [10]2 years ago
3 0

Answer:

T=56.77s

Explanation:

We must use the formula for centripetal acceleration:

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

We know the radius <em>r</em> and we want is to obtain a centripetal acceleration equal to <em>g. </em>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 <em>T</em> 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

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