Halliday, Resnick & Walker — Rotation: Problem Problem_6

CALC The angular position of a point on the rim of a rotating wheel is given by \(\theta = 4.0t - 3.0t^2 + t^3\), where \(\theta\) is in radians and \(t\) is in seconds. What are the angular velocities at (a) \(t = 2.0\text{ s}\) and (b) \(t = 4.0\text{ s}\)? (c) What is the average angular acceleration for the time interval that begins at \(t = 2.0\text{ s}\) and ends at \(t = 4.0\text{ s}\)? What are the instantaneous angular accelerations at (d) the beginning and (e) the end of this time interval?