Tubular Tire
Uniform Circular Motion Space Station question.?
A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire). The circle formed by the tube has a diameter of about 1.1km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0g) is to be felt?
Please explain as in much detail as possible.
You want the centripetal acceleration to equal the acceleration of gravity at the surface of the earth. This will of course only apply at the outer edge of the station and will decrease as you move towards the center.
g = acceleration of gravity = 9.81 m/s^2
a = centripetal acceleration = v^2/r
9.81 = v^2/r
r = radius of station = 1.1/2 = 0.55 km = 550 m
v = SQRT(9.81*r) = SQRT(5395.5) = 73.45 m/s
To get the rotation speed we need to know the time it takes the station to turn through one revolution. This is just the circumference divided by the speed we just calculated.
c = circumference of station = 2*pi*r = 3455.75 m
Period = P = c/v = 3455.75/73.45 = 47.05 seconds
So the station must rotate once every 47.05 seconds. To get the number of rotations per day we can calculate the number of seconds in a day and divided by the period we just calculated.
S = number of seconds in a day = 24*60*60 = 86400 seconds
Number of revolutions per day = S/P = 86400/47.05 = 1836.5
So the station must rotate approximately 1836 times a day in order to maintain an artificial gravity equal to that of gravity at the surface of the earth.
Installing a Tubular Tire on a Bicycle Wheel Part 2 of 2
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