**a-**

Angular acceleration:

$\overline{){\mathbf{a}}{\mathbf{=}}\frac{\mathbf{d}{\mathbf{\omega}}_{\mathbf{z}}\mathbf{\left(}\mathbf{t}\mathbf{\right)}}{\mathbf{d}\mathbf{t}}}$

$\mathit{a}\mathbf{=}\frac{\mathbf{d}}{\mathbf{d}\mathbf{t}}\mathbf{(}\mathit{\gamma}\mathbf{-}\mathit{\beta}{\mathit{t}}^{\mathbf{2}}\mathbf{)}$

A fan blade rotates with angular velocity given by *ω** _{z}*(

a- Calculate the angular acceleration as a function of time *t* in terms of *β* and *γ*. Express your answer in terms of some or all of the variables *β*, *γ*, and *t*.

b- Calculate the instantaneous angular acceleration *α** _{z}* at

c- Calculate the average angular acceleration *α*_{av−}* _{z}* for the time interval