CALC? A roller in a printing press turns through an angle ?(t) given by ?(t) = ?t2 - ?t3, where ? = 3.20 rad/s2 and ? = 0.500 rad/s3. (a) Calculate the angular velocity of the roller as a function of time. (b) Calculate the angular acceleration of the roller as a function of time. (c) What is the maximum positive angular velocity, and at what value of t does it occur?

Solution 64P Step 1: 2 3 a) P rovided, angular displacement, (t) = t - t Taking the first derivative of with respect to time we get, 2 ’ (t) = 2t - 3 t Therefore, the angular velocity of the roller as a function of time, (t) = ’ (t) = 2t - 3 t 2 3 Provided, = 3.20 rad/s and 0.500 rad/s (t) = (2× 3.20 rad/s ) t - ( 3× 0.500 rad/s ) t 3 2 (t) = 6.40 rad/s t - 1.5 rad/s t 2 2