A boy and a girl are on a spinning merry-go-round. The boy is at a radial distance of 1.2 m from the central axis; the girl is at a radial distance of 1.8 m from the central axis. Which is true? A - Boy and girl have zero tangential and angular accelerations. B - The girl has a larger angular acceleration than the boy. C - The boy has a larger tangential acceleration than the girl. D - The boy has a larger angular acceleration than the girl. E - The girl has a larger tangential acceleration than the boy.

Question

Physics

Susan Jimenez

15 August, 15:30

A boy and a girl are on a spinning merry-go-round. The boy is at a radial distance of 1.2 m from the central axis; the girl is at a radial distance of 1.8 m from the central axis. Which is true? A - Boy and girl have zero tangential and angular accelerations. B - The girl has a larger angular acceleration than the boy. C - The boy has a larger tangential acceleration than the girl. D - The boy has a larger angular acceleration than the girl. E - The girl has a larger tangential acceleration than the boy.

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Answers (1)

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Tony Horton · Answer 1

E) True. The girl has a larger tangential acceleration than the boy.

Explanation:

In this exercise they do not ask us to say which statement is correct, for this we propose the solution to the problem.

Angular and linear quantities are related

v = w r

a = α r

the boy's radius is r₁ = 1.2m the girl's radius is r₂ = 1.8m

as the merry-go-round rotates at a constant angular velocity this is the same for both, but the tangential velocity is different

v₁ = w 1,2 (boy)

v₂ = w 1.8 (girl)

whereby

v₂> v₁

reviewing the claims we have

a₁ = α 1,2

a₂ = α 1.8

a₂> a₁

A) False. Tangential velocity is different from zero

B) False angular acceleration is the same for both

C) False. It is the opposite, according to the previous analysis

D) False. Angular acceleration is equal

E) True. You agree with the analysis above,