4-72. To produce artificial gravity on a space colony, it is proposed that the colony should rotate. Suppose that the acceleration required is equal in magnitude to the acceleration due to gravity on the earth. For a colony that is 1.0 km in diameter, determine the frequency of rotation, the period of rotation, as well as the speed of a person at the edge of the colony (relative to the centre of the colony). [Ans. 2.2 x 10 2 Hz; 45 s; 7.0 x 101 m/s]


ac = v2/r
a = 9.8 m/s2
r = 0.5X103 m

So ac = 9.8 m/s2 = (v2)/0.5X103 m
v2 = 4900
v = 70 m/s

The time to make one revolution (the period T), where D is the diameter, is:

(A)   pD/v
(B)    D/v
(C)   pDv