Physics problem: Harmonia Station spins to generate gravity. If the rings are a mile in diameter, how fast (in RPMs) does it have to spin to generate 1g?
@Madagascar_Sky That's not what I got. Can we get a third opinion?
@peterdrake
Oh, sorry, forgot it's diameter. Is it 0.168319 RPM?
@Madagascar_Sky I don't think so, but I may be wrong.
SpinCalc says if the rings are 0.5 miles in radius then 1.054 rpm will give you 1 g.
@nyrath @Madagascar_Sky I plugged numbers into the formulae here:
Adjusting for imperial units and plugging into Python:
from math import pi
r = 5280 / 2
a = 32
v = (a * r) ** 0.5
W = v / r
rpm = W * (60 / (2 * pi))
print(rpm)
I had made an error in my original paper calculation, but this gives 1.051. I'm not sure of why there's a slight discrepancy from SpinCalc's answer, but essentially a 1-mile-diameter station has to spin at about 1 rpm.
Well, without access to SpinCalc's source code, it is difficult to debug the problem. But I am inclined to respect your credentials as a CS professor and trust your answer.
@nyrath @Madagascar_Sky I'm confident in the programming, but I'm just taking the elementary physics on faith.
I re-did the calcs, the online calculator is right.
Try with a = 32.174?
Your formulas are right.
@Madagascar_Sky @nyrath Yeah, that explains it -- SpinCalc was using a more precise number for 1g acceleration.
@peterdrake
I think 0.238038 RPM.