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
*a*_{c} =* v*^{2}/*r*

*a* = 9.8 m/s^{2}

*r* = 0.5X10^{3} m

Correct.

So* a*_{c} = 9.8 m/s^{2}
= (*v*^{2})/0.5X10^{3} m

*v*^{2} = 4900

*v* = 70 m/s
The time to make one revolution (the period *T*),
where *D* is the diameter, is:

(A) p*D/v*

(B)
*D/v*

(C) p*Dv*