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1. A space station is essentially a uniform disk in orbit about a planet; its mass...

1. A space station is essentially a uniform disk in orbit about a planet; its mass when empty is M = 1.68x108 kg and its radius is 6.28 km. You want to create an artificial gravity so a worker on the outer edge of the disk feels an acceleration of 3 m/s2. Find the period of the station's rotation, in minutes; this is the time it takes for one complete revolution. Assume the worker's mass is negligible.

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Answer #1

given

radius r = 6.28 km

= 6280 m

a = 3 m/sec2

M = 1.68 x 108 kg

we have a = 2 r

3 = 2 x 6280

= ( 3 / 6280 )1/2

= 0.02185 rad/s

time period equation is T = 2 /

T = 2 x 3.14 / 0.02185

T = 287.414 sec

so the reriod of station's rotation is = 287.414 / 60

= 4.79 min

so the period of station's rotation is 4.79 min.

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