Answer
(a) $1:1$ (b) $1:2$ (c) $1:2$
Work Step by Step
(a) Angular speed is independent of distance from the axis of rotation, therefore, the angular speeds are the same and the ratio is $1:1$. (b) The linear speed of a point on a rotating object is equal to $v=r\omega$. Since Betsy's radius is twice the radius of Jason, Betsy's velocity will be twice Jason's velocity. Therefore, the ratio is $1:2$. (c) The centripetal acceleration of a point on a spinning object is equal to $a=r\omega^2$. Omega remains constant for both people. Since Betsy's radius is twice the radius of Jason, Betsy's centripetal acceleration will be twice Jason's centripetal acceleration. Therefore, the ratio is $1:2$.
