A uniform disk of 10 kg and radius 4.0 m can rotate in a horizontal plane about a vertical axis through its center. The disk is rotating at

Question

A uniform disk of 10 kg and radius 4.0 m can rotate in a horizontal plane about a vertical axis through its center. The disk is rotating at an angular velocity of 15 rad/s when a 5-kg package is dropped vertically on a point that is 2.0 m from the center of the disk. What is the angular velocity of the disk/package system

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Thu Nguyệt 5 years 2021-08-19T19:03:00+00:00 1 Answers 38 views 0

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  1. quangkhai
    0
    2021-08-19T19:04:16+00:00
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    Answer:

    18.75 rad/s

    Explanation:

    Moment of inertia of the disk;

    I_d = ½ × m_disk × r²

    I_d = ½ × 10 × 4²

    I_d = 80 kg.m²

    I_package = m_pack × r²

    Now,it’s at 2m from the centre, thus;

    I_package = 5 × 2²

    I_package = 20 Kg.m²

    From conservation of momentum;

    (I_disk + I_package)ω1 = I_disk × ω2

    Where ω1 = 15 rad/s and ω2 is the unknown angular velocity of the disk/package system.

    Thus;

    Plugging in the relevant values, we obtain;

    (80 + 20)15 = 80 × ω2

    1500 = 80ω2

    ω2 = 1500/80

    ω2 = 18.75 rad/s

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