CALC? A fan blade rotates with angular velocity given by ?z(t) = ? - ?t2, where ? = 5.00 rad/s and ? = 0.800 rad/s3. (a) Calculate the angular acceleration as a function of time. (b) Calculate the instantaneous angular acceleration ?z at t = 3.00 s and the average angular acceleration ?av-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?
Solution 4E Step 1: (a).We know that the angular acceleration can be obtained from the angular velocity by taking derivative with respect to time of the angular velocity function. (t) = dw /zt = 2t Step 2: (b). nstantaneous angular acceleration 2 (3.00) = 2(0.800)(3.00)rad/s (3.00) = 4.80 rad/s 2 Average angular acceleration z w (3.z0) w (0)/z.00 0 z ( (3.00) ) ( (0) )/3.00 rad/s 2 2 2 z (0.800)(3.00) )/3.00 rad/s z 2.40 rad/s 2