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5 September, 05:48

A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system

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  1. 5 September, 06:08
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    1.25 kgm²/sec

    Explanation:

    Disk inertia, Jd =

    Jd = 1/2 * 3.7 * 0.40² = 0.2960 kgm²

    Disk angular speed =

    ωd = 0.1047 * 30 = 3.1416 rad/sec

    Hollow cylinder inertia =

    Jc = 3.7 * 0.40² = 0.592 kgm²

    Initial Kinetic Energy of the disk

    Ekd = 1/2 * Jd * ωd²

    Ekd = 0.148 * 9.87

    Ekd = 1.4607 joule

    Ekd = (Jc + 1/2*Jd) * ω²

    Final angular speed =

    ω² = Ekd / (Jc+1/2*Jd)

    ω² = 1.4607 / (0.592+0.148)

    ω² = 1.4607/0.74

    ω² = 1.974

    ω = √1.974

    ω = 1.405 rad/sec

    Final angular momentum =

    L = (Jd+Jc) * ω

    L = 0.888 * 1.405

    L = 1.25 kgm²/sec
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