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.

Abbie’s acceleration is (1/2) Zak’s acceleration.

Explanation

1. Data:

a) ω = constant

b) Abbie: r₁ = 1 m

c) Zak: r₂ = 2 m

d) Ac₁ = ? Ac₂

2. Formulae

Ac = ω² r

3. Solution:

a) Abbie:

Ac₁ = ω² r₁  =  ω² (1m)

b) Zack:

Ac₂ = ω² r₂  = ω² (2m)

c) Divide Ac₁ / Ac₂

Ac₁ / Ac₂ =  ω² (1m) / [ω² (2m) ] = 1/2

⇒      Ac₁ = (1/2) Ac₂ = Ac₂ / 2 = 0.5 Ac₂

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