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16 August, 07:47

With the aid of a string, a gyroscope is accelerated from rest to 16 rad/s in 0.40 s. What is its angular acceleration in rad/s2? Approximately how many revolutions does it go through in the process?

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  1. 16 August, 08:11
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    Given that,

    A gyroscope accelerated from rest

    Initial angular speed ωi = 0

    The gyroscope accelerated to

    ωf = 16rad/s

    time taken t = 0.4s

    A. What is it's angular acceleration α?

    Using equation of circular motion

    ωf = ωi + αt

    16 = 0 + 0.4α

    16 = 0.4α

    then, α = 16 / 0.4

    α = 40rad/s2

    The angular acceleration is 40rad/s².

    b. Revolution θ?

    Using circular motion equation

    ωf² = ωi² + 2α∆θ

    16² = 0² + 2*40∆θ

    256 = 0 + 80∆θ

    256 = 80∆θ

    ∆θ = 256 / 80

    ∆θ = 3.2 rad.

    θf - θi = 3.2rad

    The initial revolution Is zero, since it starts from rest

    θ = 3.2rad

    We know that, 1 rev = 2πrad

    Then, θ = 3.2 rad * 1rev/2πrad

    θ = 0.51 revolution

    θ ≈ 0.5 revolution

    So, gyroscope makes an approximately 0.5 revolution in 0.4 seconds
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