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12 September, 03:29

An engine flywheel initially rotates counterclockwise at 6.69 rotations/s. Then, during 20.1 s, its rotation rate changes to 2.65 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.

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  1. 12 September, 03:42
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    Given that

    We are told to assume counterclockwise to be positive

    Then, clockwise will be negative

    initial angular velocity counterclockwise

    ωi = 6.69 rotation/sec

    1 rotation = 1 revolution = 2π rad

    Then, ωi = 6.69 * 2π rad/s

    ωi = 42.03 rad/s

    Final angular velocity clockwise

    ωf = 2.65 rotation/sec

    ωf = 2.65 * 2π rad/s

    ωf = - 16.65 rad/s

    Time taken t = 20.1s

    Now, we want to find angular acceleration, α

    Angular acceleration is given as

    α = ∆ω/∆t

    α = (ωf - ωi) / t

    α = (-16.65-42.03) / 20.1

    α = - 58.68 / 20.1

    α = - 2.92 rad/s²

    So, the angular acceleration is - 2.92 rad/s²
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