Problem 4-72 Centripetal acceleration

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. \(2.2 \times 102\; Hz;\) \(45\; s;\) \(7.0 \times 101 \;m/s\)]

The expression for centripetal acceleration is:

(A)    \(a_c = v/r\)

(B)    \(a_c = v^2/r\)

(C)    \(a_c = v^2r\)