A fan blade rotates with angular velocity given by ωz (t) = γ - β t2. part a calculate the angular acceleration as a function of time. express your answer in terms of the variables β, γ, and t. αz (t) = submitmy answersgive up part b if γ = 5.35 rad/s and β = 0.810 rad/s3, calculate the instantaneous angular acceleration αz at t = 3.00 s.

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Physics

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9 July, 18:14

A fan blade rotates with angular velocity given by ωz (t) = γ - β t2. part a calculate the angular acceleration as a function of time. express your answer in terms of the variables β, γ, and t. αz (t) = submitmy answersgive up part b if γ = 5.35 rad/s and β = 0.810 rad/s3, calculate the instantaneous angular acceleration αz at t = 3.00 s.

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Kennedi Ryan · Answer 1

Given:

w = z (t) = γ - β*t^2

Differentiating both sides with respect to t, we get:

α = z (t) = - 2βt

Given: γ = 5.35 rad/s and β = 0.810 rad/s3

so, For t = 3 sec,

angular acceleration = - 2 * 0.810 * 3 = - 4.86