A fan blade rotates with angular velocity given by ωz(t)= γ − β t2, where γ = 4.90 rad/s and β = 0.750 rad/s3 . part a calculate the angular acceleration as a function of time.

The angular velocity as a function of time is given by
[tex]\omega (t)=\gamma-\beta t^2[/tex]
where [tex]\gamma=4.90 rad/s[/tex] and [tex]\beta=0.750 rad/s^3[/tex]. The angular acceleration as a function of time is equal to the derivative of the angular velocity. If we calculate the derivative of w(t), we find:
[tex]\alpha(t)= \frac{d\omega}{dt} =-2\beta t[/tex]
and this is the angular acceleration of the fan blade.

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shirleywashington shirleywashington · Answer 2 · 2019-04-26T18:43:33+02:00

Answer:

Angular acceleration, α = -2βt

Explanation:

Angular velocity of fan is [tex]\omega_{z(t)}=\gamma -\beta t^2[/tex]

[tex]\gamma=4.90\ rad/s[/tex]

[tex]\beta=0.750\ rad/s^3[/tex]

Angular acceleration is given by :

[tex]\alpha=\dfrac{d\omega}{dt}[/tex]

[tex]\alpha=\dfrac{d(\gamma -\beta t^2)}{dt}[/tex]

[tex]\alpha=-2\beta t[/tex]

Hence, the above equation is the angular acceleration as a function of time.