Question

Mary and her younger brother Alex decide to ride the carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 2.0 m from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 1.3 m from the center. The carousel takes 5.3 s to make each complete revolution.a) What is Mary's angular speed and tangential speed vM?b) What is Alex's angular speed and tangential speed vA?

Answer 1

Explanation:

Given

Marry sits at a distance of $r_1=2 m$

Alex sits at a distance of $r_2=1.3 m$

Time Period of carousel $T=5.3 s$

Let angular speed of carousel \omega

$\omega T=2\pi$

$\omega =\frac{2\pi }{T}$

$\omega =\frac{2\pi }{5.3}$

$\omega =1.18 rad/s$

(a)Mary angular speed and tangential

angular speed of Mary $=1.18 rad/s$

Tangential Speed $v=\omega \times r_1$

$v=\omega \times r_1=1.18\times 2=2.37 m/s$

(b)Angular speed of Alex''s will be equal to carousel $=1.18 rad/s$

Tangential speed of Alex$=\omega \times r_2=1.18\times 1.3=1.53 m/s$