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26 December, 05:54

A carousel has a radius of 1.70 m and a moment of inertia of 110 kg · m2. A girl of mass 44.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.40 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop?

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  1. 26 December, 07:53
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    Initial moment of inertia of the carousel + girl

    I₁ = 110 + 44 x 1.7²

    = 110 + 127.16

    = 237.16 kgm².

    final moment of inertia of carousel + girl

    I₂ = 110 + 44 x d²

    applying law of conservation of angular momentum

    I₁ ω₁ = I₂ω₂

    ω₁ and ω₂ are angular velocities of the carousel before and after.

    237.16 x 3.4 = (110 + 44 x d²) x 5.4

    806.34 = 594 + 237.6 d²

    237.6 d² = 212.34

    d²=.8936

    d =.9453 m
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