Question

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.

Answer 1

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

Step-by-step 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