Question

Mary and her younger brother Alex decide to ride the 26-foot-diameter carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 11 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 7 feet from the center.

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

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

Answer 1

Anguler speed e defneed as the rate of change of anguler a desplacement with time Now, let us consider the Let o be the center Mary resades at M, while alexa sendes at A. تل agram

9 o Here el OA = OA-7 SA And OM OM '= 11 st. Le led due to sotelion, the position of Many changes changes from to me Whete the position of Alexa changes from A Ą A) you in the figure, lenter length MM o A A But the angulas displecement for at en same as the angular displacement intomi e (=0) If & this position change occured in teme it, then, angular vebaly of Al o O t fox Lenien velocity of in VAZ AAl length

2 Angular velocity of Mary Me a A wм VARUM :MMJAR Lenein velocity of Mary us MM' length t Fron 0 and ( we can say that WMF Ang Tumawa o + 1+ Let wm=WA w. velocity angular velocity x radius of rotaton. We know that lenien > So heslenier velocty of Alexa its) - 7w F-0z7ft VA = wy JA lenia velocity of Mery en OM= wx OM - la ft Vm=

Reyes VM 11 w I w N VA 7 w Vor = 14 ora z tos 7 A Vm= 1.57 VABA)
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