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A spinning disk is rotating at a rate of 5 rad/s in the positive counterclock-wise direction. If the disk is subjected to an angular acceleration in the counterclock-wise direction at a rate of 2 rad/s2, Find the wheel's angular velocity in rad/s after 4 s.

Answer :

cjrodriguez89

Answer:

ωf = 13 rad/s

Explanation:

  • The angular acceleration, by definition, is just the rate of change of the angular velocity with respect to time, as follows:
  • α = Δω/Δt = (ωf-ω₀) / (tfi-t₀)
  • Choosing t₀ = 0, and rearranging terms, we have

       [tex]\omega_{f} = \omega_{o} + \alpha *t (1)[/tex]

       where ω₀ = 5 rad/s, t = 4 s, α = 2 rad/s2

  • Replacing these values in (1) and solving for ωf, we get:

        [tex]\omega_{f} = 5 rad/s + (2 rad/s2*4 s) = 13 rad/s (2)[/tex]

  • The wheel's angular velocity after 4s is 13 rad/s.

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