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15 June, 21:33

An airliner arrives at the terminal, and the engines are shut off. The rotor of one of the engines has an initial clockwise angular velocity of 2000 rad/s. The engine's rotation slows with an angular acceleration of magnitude 80.0 rad/s2. (a) Determine the angular velocity after 10.0 s. (b) How long does it take the rotor to come to rest?

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  1. 16 June, 00:30
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    (a) ωf = 1200 rad/s

    (b) t = 25 s

    Explanation:

    Kinematic Equation to the rotor

    ωf = ω₀ + α*t Formula (1)

    Where:

    α : angular acceleration (rad/s²)

    t : time interval (s)

    ω₀ : initial angular velocity (rad/s)

    ωf : final angular velocity (rad/s)

    (a) Angular velocity after 10.0 s

    Data

    α = - 80 rad/s²

    t = 10 s

    ω₀ = 2000 rad/s

    We apply the formula (1):

    ωf = ω₀ - α*t

    ωf = 2000 - 80 * (10)

    ωf = 2000 - 800

    ωf = 1200 rad/s

    (b) Time the rotor stops

    Data

    α = - 80 rad/s²

    ω₀ = 2000 rad/s

    ωf = 0

    We apply the formula (1):

    ωf = ω₀ - α*t

    0 = 2000 - 80 * (t)

    80 * (t) = 2000

    t = 2000 / 80

    t = 25 s
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