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]
ACCUMULATED SOLUTION
ac = v2/r
a = 9.8 m/s2
r = 0.5X103 m
Correct.
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