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 1.4 m from the center. The carousel takes 4.2 s to make each complete revolution.
(a) What is Mary's angular speed M and tangential speed vM?
M = rev/s
vM = m/s

(b) What is Alex's angular speed A and tangential speed vA?
A = rev/s
vA = m/s

Answer 1

Mary and her younger brother Alex decide to ride the carousel at the State Fair, Mary's and Alex's  angular speed M and tangential speed vM is mathematically given as

Mary's and Alex's  angular speed=1.43

Tangential speed mary=3.22 m/s

Tangential speed alex =2.260m/s

What is Mary's and Alex's angular speed M and tangential speed vM?

Generally, the equation for angular speed is mathematically given as

$w=2\pi /T\\\\Therefore\\\\w=2\pi/3.9$

w = 1.61 rev/see 3.9

Centripetal acc mary = v^2/r

Centripetal acc mary  = w^2r

Centripetal acc mary = w^2x 2m

Centripetal acc. of Alex = w²x L.u

Therefore

$\frac{(ac) mary }{(ac) plex}= 1.43$

Hence

tang. speed V=Wr

tang. speed of mary = 1.61x2 = 3.22 m/s

tang. speed of Alex: 1.61X1·4 =2.260m/s

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