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

Step-by-step 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 =(2\pi )/(T)`

`\omega =(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 * r_1`

`v=\omega * r_1=1.18* 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 * r_2=1.18* 1.3=1.53 m/s`