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27 May, 13:45

We can model a small merry-go-round as a uniform circular disk with mass 88 kg and diameter 1.8 m. How many 22 kg children need to ride the merry-go-round, standing right at the outer edge, to double the moment of inertia of the system?

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  1. 27 May, 17:15
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    n = 2 children

    Explanation:

    Given

    M = 88 Kg

    D = 1.8 m ⇒ R = D/2 = 1.8 m/2 = 0.9 m

    m = 22 Kg

    n = ?

    We apply the formula

    Icm = M*R²/2

    ⇒ Icm = (88 Kg) * (0.9 m) ²/2 = 35.64 Kg*m²

    If

    I = 2*Icm = 2*35.64 Kg*m² = 71.28 Kg*m²

    we apply Steiner's Theorem as follows

    I = Icm + n*m*R²

    ⇒ n = (I - Icm) / (m*R²)

    ⇒ n = (71.28 Kg*m² - 35.64 Kg*m²) / (22 Kg * (0.9 m) ²)

    ⇒ n = 2 children
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