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)    $a_c = v^2r$