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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.(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.

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Answer:

[tex]\omege_A=\omega_M[/tex]

[tex]v_M=1.6v_A[/tex]

Explanation:

A denotes Alex

M denotes Mary

r = Distance from center

Mary and Alex will have the equal displacements in equal interval of time as they are in uniform circular motion. So,

[tex]\omega_A=\omega_M[/tex]

Tangential speed speed is given by

[tex]\dfrac{v_M}{v_A}=\dfrac{r_M\omega_M}{r_A\omega_A}\\\Rightarrow \dfrac{v_M}{v_A}=\dfrac{r_M}{r_A}\\\Rightarrow \dfrac{v_M}{v_A}=\dfrac{8}{5}\\\Rightarrow \dfrac{v_M}{v_A}=1.6\\\Rightarrow v_M=1.6v_A[/tex]

The tangential speed of Mary is [tex]v_M=1.6v_A[/tex]

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