A proposed space station includes living quarters in a circular ring 64.0 m in d
ID: 1362359 • Letter: A
Question
A proposed space station includes living quarters in a circular ring 64.0 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth?
It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution (mean sidereal day)
Assume the earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the earth to the object makes an angle of 42.0° with the axis of rotation. The radius of the earth is 6.37×103 km.
What is the acceleration of the object on the surface of the earth in the previous problem?
Explanation / Answer
accleration due to gravity g = r w^2
W = sqrt(g/r)
W^2 = 9.8/32
W = 0.553 rad/s
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V = 2pi R/T
V = 2*3.14 * 32/(86164)
V = 0.0023 m/s
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V = r W
V = 32* 0.553
V = 17.7 m/s
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g = GM./r^2
g = 6.67 e -11 *5.97 e 24/(6.37 e 6)^2
g = 9.81 m/s^2
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