Question

A fan blade rotates with angular velocity given by wu (t) =Y - Bt2, where Y = 5.00 rad/s and p = 0.800 rad/s3.

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

(b) Calculate the instantaneous angular acceleration a z at t = 3.00 s and the average angular acceleration a avc for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why are they different?

Answer 1

(a) $\alpha(t)=-2Bt.$

(b) $\alpha (3)=-4.8\text{ rad/s}^2.\\ \alpha(0)=0.\\ \alpha_\text{avg}=(\alpha(3)-\alpha(0))/(3-0)=1.6\text{ rad/s}^2.$

They are different because they are calculated differently.