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21 June, 07:02

Two disks are mounted (like a merry-go-round) on low friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia 3.30 kg·m² about its central axis, is set spinning counterclockwise at 450 rev/min. The second disk, with rotational inertia 6.60 kg·m² about its central axis, is set spinning counterclockwise at 900 rev/min. They then couple together.

(a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 900 rev/min,

what are their:

(b) angular speed and

(c) direction of rotation after they couple together?

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Answers (1)
  1. 21 June, 10:49
    0
    a) 750 rev/min

    b) 450 rev/min

    c) clockwise direction

    Explanation:

    We are given;

    Rotational inertia of first disk; I_1 = 3.3 kg. m²

    Angular velocity of first disk; ω_1 = 450 rev/min

    Rotational Inertia of second disk; I_2 = 6.6 kg. m²

    Angular velocity of second disk; ω_2 = 900 rev/min

    Total rotational inertia; I_tot = 3.3 + 6.6 = 9.9 kg. m²

    Since they couple together, we have;

    I_tot * ω = (I_1 * ω_1) + (I_2 * ω_2)

    Plugging in values, we have;

    9.9ω = (3.3 * 450) + (6.6 * 900)

    9.9ω = 7425

    ω = 7425/9.9

    ω = 750 rev/min

    b) now, we are told the second disk is spinning clockwise, thus we have;

    I_tot * ω = (I_1 * ω_1) - (I_2 * ω_2)

    9.9ω = (3.3 * 450) - (6.6 * 900)

    9.9ω = - 4455

    ω = - 4455/9.9

    ω = - 450 rev/min

    The minus sign indicates a clockwise direction.
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