# A question on centrifugal artifical gravity

1. Jul 31, 2013

### grubbyknickers

How fast would a hollow cylindrical object seven miles in diameter need to spin to maintain earth gravity on the interior surface?

2. Jul 31, 2013

### Staff: Mentor

Welcome to the PF.

What is the context of the question? Is this for schoolwork? What do you know already about centriptal forces?

3. Jul 31, 2013

### grubbyknickers

the question does not relate to schoolwork, I'm working on a science fiction novel and my math skills are inferior so I can't crack a book and easily solve the equation myself.
I need to know the rpm the cylinder would need to spin at to maintain normal earth gravity (would it be a four minute revolution, a half hour revolution?).

4. Aug 1, 2013

### technician

Do you recognise the equation ω2r for calculating centripetal acceleration
Also, when you come to do the calculation I would suggest that you give the radius in metres rather than miles.

5. Aug 1, 2013

### jfizzix

If the space station is 7 miles in diameter, it is 3.5 miles in radius.

If we assume that we want to feel Earth-level artificial gravity at this distance from the center, we want the centripedal acceleration of a point on this cylinder to be the same as the acceleration due to gravity. In short,

$a_{edge} = g$
but
$a_{edge} = R \omega^{2}$
where R is the radius of the station (3.5 miles or 5607 meters) and omega is the angular velocity of the space station in radians per second.

Then we solve for $\omega$, finding that
$\omega=\sqrt{\frac{g}{R}}$
so that $\omega$ is about 6.64thousandths of a revolution per second or about 0.40 revolutions per minute.

6. Aug 1, 2013

### jfizzix

hope that helps:)

7. Aug 1, 2013

### jfizzix

4/10 revolutions per minute means 10/4 minutes per revolution or about 2 1/2 minutes per revolution