# Problem: A fan blade rotates with angular velocity given by ωz(t) = γexttip{gamma }{gamma} - βexttip{eta }{beta}t2.a) Calculate the angular acceleration as a function of time.b) If γexttip{gamma}{gamma_1} = 5.05 rad/s and βexttip{eta}{beta_1} = 0.805 rad/s3 , calculate the instantaneous angular acceleration αz at t exttip{t}{t_0}= 3.10 s .c) If γ exttip{gamma}{gamma_1} = 5.05 rad/s and βexttip{eta}{beta_1} = 0.805 rad/s3 , calculate the average angular acceleration αav - z for the time interval t = 0 to t exttip{t}{t_0}= 3.10 s .

###### Problem Details

A fan blade rotates with angular velocity given by ωz(t) = γexttip{gamma }{gamma} - βexttip{eta }{beta}t2.
a) Calculate the angular acceleration as a function of time.
b) If γexttip{gamma}{gamma_1} = 5.05 rad/s and βexttip{eta}{beta_1} = 0.805 rad/s3 , calculate the instantaneous angular acceleration αz at t exttip{t}{t_0}= 3.10 s .
c) If γ exttip{gamma}{gamma_1} = 5.05 rad/s and βexttip{eta}{beta_1} = 0.805 rad/s3 , calculate the average angular acceleration αav - z for the time interval t = 0 to t exttip{t}{t_0}= 3.10 s .