Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel a

Question

Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 8 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 5 feet from the center.

(a) What is Mary's angular speed M compared to that of Alex's angular speed A? Give your answer as a multiple of A.
M = 1 A

(b) What is Mary's tangential speed vM compared to that of Alex's tangential speed vA? Give your answer as a multiple of vA.
vM = 2 vA

Explanation / Answer

a) Since they are both in the same carousel the angular speed of both is the same because the angular speed denpends on how much time does the carousel spends on 1 rev so

M = 1 A

b)

we know that v=R then:

VM=Rm and VA=Ra

since the angular speed is the same for both

VM/Rm=VA/Ra

VM=8VA/5

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