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Two children are riding on a merry-go-round that is rotating with a constant angular speed. Abbie is one meter from the center of the merry-go-round, whereas Zak is two meters from the center. Abbie’s acceleration is ___________ Zak’s acceleration. Two children are riding on a merry-go-round that is rotating with a constant angular speed. Abbie is one meter from the center of the merry-go-round, whereas Zak is two meters from the center. Abbie’s acceleration is ___________ Zak’s acceleration. a quarter of twice equal to half of four times

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Answer:

The acceleration of Abbie is half of the Zak's.

Explanation:

The centripetal acceleration of an object on a circular path is given by :

[tex]a=r\omega^2[/tex]

Two children are riding on a merry-go-round that is rotating with a constant angular speed. Let [tex]r_1[/tex] is distance of Abbie from the merry-go-round and [tex]r_2[/tex] is distance of Zak's from the merry-go-round. Acceleration of Abbie is :

[tex]a_1=r_1\omega^2[/tex] ...... (1)

[tex]r_1=1\ m[/tex]

Acceleration of Zak's is :

[tex]a_2=r_2\omega^2[/tex] .......(2)

[tex]r_2=2\ m[/tex]

Dividing equation (1) and (2) we get :

[tex]\dfrac{a_1}{a_2}=\dfrac{r_1}{r_2}\\\\\dfrac{a_1}{a_2}=\dfrac{1}{2}\\\\a_1=\dfrac{a_2}{2}[/tex]

So, the acceleration of Abbie is half of the Zak's.

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