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dotlin's avatar

How to calculate the rate of rotation, in revolutions per minute.

Asked by dotlin (419points) July 21st, 2010

Calculate the rate of rotation, in revolutions per minute, of a space station which is 120 m. in diameter, if normal gravity (g = 9.8m/s) is maintained at the edge.

Could you explain what this question is asking as I’m not too sure and then how to answer this.

No it’s not homework it would be summer holidays anyway I just want to know.

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7 Answers

cockswain's avatar

I’m going with 1.56 revs/min.

Circumference = pi*d = 376.8 m

Rate of rotation = 9.8 m/s, so it takes 38.4s to complete one rev.
60/38.4 = 1.56

Zyx's avatar

It’s asking you to convert the diameter and the required centrifugal force into the speed the station needs to spin. There’s some rule some other guy here will probably give you and that’s all the info you really need.

Ivan's avatar

@cockswain

The rate of rotation is not 9.8 m/s.

Imagine a giant cylinder, spinning about its axis. If you’re inside the cylinder, your inertia will fling you to the walls of the cylinder, sort of like clothes in a dryer. The faster it spins, the more you will be thrown to the edges. If it spins fast enough, a sort of artificial gravity will be observed. You could walk around the inner walls of the cylinder as if there were normal gravity. The question is asking you to calculate how fast the cylinder has to spin to achieve this effect.

cockswain's avatar

OK. Then how does one solve this problem?

But if the question had asked “How many revs per minute is a 120 meter space station completing at a rotational rate of 9.8m/s?”, I had it right.

Ivan's avatar

@cockswain

Acceleration around a circle is given by (v^2)/r, where v is the tangential velocity, and r is the radius of the circle. We desire an acceleration of 9.8 m/s/s, and we know the radius is 60 m, so…

9.8 m/s/s = (v^2)/60, which yields v = ~24.25 m/s.

Now, we know that the circumference of the circle is given by 2πr, or in this case 2π(60), which yields C = ~377 m.

Finally, dividing the tangential velocity by the circumference gives you your angular velocity. 24.25/377 = ~0.064 rev/s.

Converting this to the desired units gives us ~3.86 rev/min.

cockswain's avatar

Slick. Good job.

dotlin's avatar

@cockswain
I’m not quite getting why (v^2)/r is the equation, I’m just not intuitively understanding why the equation is so..

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