Space station question

Andrew

Andrew

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I remember in 2001 (the film rather than the year) that the space station rotates to give the occupants gravity.

So, when bored I wondered what speed it spin to give 1 earth gravity. Bear with me:

Using

a = w 2 r

w in rad/sec

I reckon a 100 metre radius station would have to rotate at 3.15 rpm giving a linear velocity of 33m/s.

A 200m radius would be 2.14rpm, 45 m/s. (Big rounding errors as can't find a calculator).

Using v=wr to sub into the other equation I get:

ar = v 2

So I think the bigger the station gets the faster you have to be travelling to get 1 gravity.

Some one put me out of my misery and check my calculations as I know there are brainy engineering and physics type people here.

Thanks for your indulgence.

 
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Ironically, you posted this about the same time I was playing the LP soundtrack from 2001: A Space Odyssey, particularly to hear the Danube Waltz, the music that accompanies the approach to the rotating space station.

As for your question, I have no direct answers, but there are some websites that may help:

 
I think what JohnnyB is trying to say is that a 15cm radius station rotates at 33 1/3 rpm.

 
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I am pretty sure there is a problem with v=wr to replace w^2r as v^2.

W^2r=. wwr= wv. If v = wr

 
mathman said:
I am pretty sure there is a problem with v=wr to replace w^2r as v^2.

W^2r=. wwr= wv. If v = wr
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w = v/r then w 2 = v 2 / r 2

a = w 2 r or a/r = w 2 = v2 / r2 multiply both sides by r 2

and you get a x r = v 2

And it fits roughly with the velocity worked out using the circumferance. Or I may well be wrong. I am running out of old envelopes.

 
cynic said:
I think what JohnnyB is trying to say is that a 15cm radius station rotates at 33 1/3 rpm.
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Back in college we used a cheap BSR turntable to test which of four kittens was the most tenacious against 33-1/3 RPM centripetal force. Last kitten thrown off won. His prize? Another ride with all the losing kittens.

Speaking of turntables, the late John Michell, founder of Michell Engineering, a British high end turntable company, built the model used for the spaceship Discovery in 2001: A Space Odyssey. According to the company history, the Discovery inspired his turntable designs.

mj_disc_DONE7.JPG


A few years ago there was a thread that showed Jol at home in front of his stereo rig. His turntable was a JA Michell Gyrodec.

Gyro-se-web-300x200.jpg


Another high end turntable/tonearm company is SME Limited, which originally stood for Scale Model Equipment Company Ltd. I think they also made some iconic models in the old days but I've forgotten--or never knew--what they are, but here's their top line turntable.

Model30-12thumb.jpg


 
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I'm envious at all of you math experts. I've always leaned more toward literature and logic/analytic philosophy, but math is just too complex for me. My poor memory can never seem to retain or recall all of the formulas necessary to perform the necessary calculations or able to memorize the symbolic shorthand. Perhaps it's true after all that artists are not wired for math.

On another note, what is one "earth gravity"? To what kind of unit does the reference apply?

 
FGJ said:
I'm envious at all of you math experts. I've always leaned more toward literature and logic/analytic philosophy, but math is just too complex for me. My poor memory can never seem to retain or recall all of the formulas necessary to perform the necessary calculations or able to memorize the symbolic shorthand. Perhaps it's true after all that artists are not wired for math.

On another note, what is one "earth gravity"? To what kind of unit does the reference apply?
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9.8 metres per second per second, the acceleration of a body dropped in a vacuum. About 5 metres in first second, 20 after 2 seconds according to the formula,

d=vt + 1/2a t 2 .

There is no such thing as a mathematical mind or an artistic one, it's all just training. You could do it if you really wanted or needed to, ordinary language is much more complex that maths.. (Note the s, please!)

 
Thanks, Andrew, that's encouraging, and I'm certain you're probably entirely correct. Were I not already far along in life with no time on my hands, I'd like to actually try to learn something beyond basic math. As is often the case, I rarely have any need for anything beyond basic math, and perhaps that's the source of my apathy and laziness (and I suspect most others unfortunately share my excuse as well).

My only regret is that my apparent lack of math skills make it difficult for me to wade through more complex symbolic logic. Propositional logic and analytic philosophy rooted in language and semantics seems to come more easily to me, but as soon as a string of symbolic logic gets too lengthy, my mind has difficulty handling it.

 
FGJ said:
Thanks, Andrew, that's encouraging, and I'm certain you're probably entirely correct. Were I not already far along in life with no time on my hands, I'd like to actually try to learn something beyond basic math. As is often the case, I rarely have any need for anything beyond basic math, and perhaps that's the source of my apathy and laziness (and I suspect most others unfortunately share my excuse as well).

My only regret is that my apparent lack of math skills make it difficult for me to wade through more complex symbolic logic. Propositional logic and analytic philosophy rooted in language and semantics seems to come more easily to me, but as soon as a string of symbolic logic gets too lengthy, my mind has difficulty handling it.
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I feel the same way. While I was in high school, I struggled with trigonometry and biology; the next stage would have been calculus and physics. My brain wasn't ready for them back then, but I wish I could have eased into it because I would probably have loved it, possibly designing audio equipment or designing sound systems where calculations for acoustics of odd-shaped spaces walled by extreme ranges of reflective and absorptive materials would have been part of the job.

 
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