A fan blade rotates with angular velocity given by ω_{z}(t) = γ - βt^{2}.

a) Calculate the angular acceleration as a function of time.

b) If γ = 5.05 rad/s and β = 0.805 rad/s^{3} , calculate the instantaneous angular acceleration α_{z} at t = 3.10 s .

c) If γ = 5.05 rad/s and β = 0.805 rad/s^{3} , calculate the average angular acceleration α_{av - z} for the time interval t = 0 to t = 3.10 s .