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23 August, 08:04

Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at 8.94 rad/s, but the other one rotates in the opposite direction at 3.42 rad/s.

Required:

Calculate the magnitude of the net angular momentum of the system.

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Answers (1)
  1. 23 August, 11:38
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    the angular momentum is 1015.52 kg m²/s

    Explanation:

    given data

    mass of each flywheel, m = 65 kg

    radius of flywheel, r = 1.47 m

    ω1 = 8.94 rad/s

    ω2 = - 3.42 rad/s

    to find out

    magnitude of the net angular momentum

    solution

    we get here Moment of inertia that is express as

    I = 0.5 m r² ... 1

    put here value and we get

    I = 0.5 * 65 * 1.47 * 1.47

    I = 70.23 kg m²

    and

    now we get here Angular momentum that is express as

    L = I * ω ... 2

    and Net angular momentum will be

    L = 2 * I x ω1 - I * ω2

    put here value and we get

    L = 2 * 70.23 * 8.94 - 70.23 * 3.42

    L = 1015.52 kg m²/s

    so

    the angular momentum is 1015.52 kg m²/s
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