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 se 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 (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

angular velocity = angular distance / time

both alex and mary will cover equal distance in same time so,

M = 1 * A

tangential speed = 2 * pi * radius / time

vM = 2 * pi * rM / time

vA = 2 * pi * rA / time

vM = (rM / rA) * vA

rM = 17/2 foot or 2.5908 m

rA = 5 feet or 1.524 m

vM = (2.5908 / 1.524) * vA

vM = 1.7 vA

angular distance = linear distance / radius

angular distance = 1.89 / 0.44

angular distance = 4.295 rad or 246.085 degree

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