Halliday, Resnick & Walker — Rotation: Problem 57

57 A pulley, with a rotational inertia of \(1.0 \times 10^{-3} \text{ kg}\cdot\text{m}^2\) about its axle and a radius of \(10 \text{ cm}\), is acted on by a force applied tangentially at its rim. The force magnitude varies in time as \(F = 0.50t + 0.30t^2\), with \(F\) in newtons and \(t\) in seconds. The pulley is initially at rest. At \(t = 3.0 \text{ s}\) what are its (a) angular acceleration and (b) angular speed?