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A 21-kg child starts at the center of a playground merry-go-round that has a radius of 1.7 m and rotational inertia of 500 kg⋅m2 and walks out to the edge. The merry-go-round has a rotational speed of 0.20 s−1 when she is at the center.What is its rotational speed when she gets to the edge?

Respuesta :

Answer:

 [tex]\omega_2 = 0.178\ rad/s[/tex]

Explanation:

given,  

radius of merry - go - round = 1.7 m  

mass of children = 21 Kg

rotational inertia of merry go round = 500 Kg.m²

rotational speed = 0.2 s⁻¹

I₁ = 500 Kg.m²

I₂ = I₁ + m R²

I₂ = 500 + 21 x 1.7²

I₂ = 560.69 Kg.m²

using equation

  I₁ ω₁ = I₂ ω₂

 500 x 0.2  = 560.69 ω₂

 [tex]\omega_2 = \dfrac{500 \times 0.2}{560.69}[/tex]

 [tex]\omega_2 = 0.178\ rad/s[/tex]

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