A fan blade rotates with angular velocity given by omega z(t)=gamma- beta t2 Cal

Question

A fan blade rotates with angular velocity given by omega z(t)=gamma- beta t2 Calculate the angular acceleration as a function of time. alpha z(t)=-2( beta )t For the next two parts assume that the constants gamma and beta are defined as follows: gamma = 4. 90rad/s beta = 0. 820rad/s3 A fan blade rotates with angular velocity given by omega z(t)=gamma- beta t2 Calculate the instantaneous angular acceleration alpha z at t0=3. 0s. Calculate the average angular acceleration alpha av-Z for the time interval t = 0 to t0 = 3. 0s

Explanation / Answer

angular accelaration = dw/dt = -2(beta)t

b) t = 3 sec

so angular acce. = -2 x 0.820 x 3 = -4.92 rad/s2

c) w(0) = 4.90 - 0.820 x 0 = 4.90 rad/s

w(3) = 4.90 - 0.820 x 3^3 = - 2.48 rad/s

average angular acc. = w(3) - w(0) /3 = -2.48 - 4.90 / 3 = - 2.46 rad/s2

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