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 = 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 = vA

Explanation / Answer

a)

each and every point of the carousel moves with same angular velocity

so mary and alex has the same angular speed

so the answer for A) is wM = wA

b) tangential speed is v = r*w

so

wM = wA

VM/rM = vA/rA

vM/8 = vA/5

vM = (8/5)*vA

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