Physics gravity Help?
A proposed space station shaped like a huge bicycle wheel with diameter of 625 m is to spin at a rate to produce "artificial gravity" for the occupants in the "rim" of the station. What should be the period of the station's rotation? Been trying to figure out this problem for 30 minutes any suggestions?
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the centrip accel = v^2/r and you want this to equal 9.8m/s/s
since r = 312.5m (use radius, not diameter) we have
v^2/312.5m = 9.8m/s/s => v = 55.3m/s
period = dist/velocity = 2 pi r/v = 2 pi x 312.5m/55.3m/s = 35.4s
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The acceleration due to gravity here on earth is 9.8 m/s^2. We need to duplicate this acceleration in the space station. Centripetal acceleration in circular motion is given by:
a = v^2/r
a = 9.8 m/s^2
r = (625/2)m = 312.5 m
9.8 m/s^2 = (v^2)/312.5 m
v^2 = 3062.5 m^2/s^2
v = 55.34 m/s
angular velocity is related to linear velocity by:
v = rw
55.34 m/s = (312.5 m)(w)
w = 0.1771 rad/s
Period is related to angular velocity by:
1/T = w/(2Pi)
T = 2Pi/w
T = 35.5 seconds