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10 September, 03:00

Three solid, uniform flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis. Two of the flywheels rotate in one direction at 3.83 rad/s; the other rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system.

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  1. 10 September, 03:13
    0
    297.77 kg m^2 / s

    Explanation:

    mass of each flywheel, m = 65 kg

    radius of flywheel, r = 1.47 m

    ω1 = 3.83 rad/s

    ω2 = - 3.42 rad/s

    Moment of inertia, I = 1/2 mr² = 0.5 x 65 x 1.47 x 1.47 = 70.23 kg m^2

    Angular momentum is defined as

    L = I x ω

    Net angular momentum

    L = 2 x I x ω1 - I x ω2

    L = 2 x 70.23 x 3.83 - 70.23 x 3.42

    L = 537.96 - 240.19

    L = 297.77 kg m^2 / s

    Thus, the angular momentum is 297.77 kg m^2 / s.
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