A question on centrifugal artifical gravity

[grubbyknickers]

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

 

[berkeman]

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

Welcome to the PF.

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

 

[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?).

 

[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.

 

[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.

 

[jfizzix]

hope that helps:)

 

[jfizzix]

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