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?
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.
@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 @Madagascar_Sky
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.