A 4-kg disk A is mounted on arm BC, which has a negligible mass. If a torque of M =

Chapter 19, Problem 19-15

(choose chapter or problem)

A 4-kg disk A is mounted on arm BC, which has a negligible mass. If a torque of \(M=\left(5 e^{0.5 t}\right) \ \mathrm{N} \cdot \mathrm{m}\), where t is in seconds, is applied to the arm at C, determine the angular velocity of BC in 2 s starting from rest. Solve the problem assuming that (a) the disk is set in a smooth bearing at B so that it moves with curvilinear translation, (b) the disk is fixed to the shaft BC, and (c) the disk is given an initial freely spinning angular velocity of \(\boldsymbol {\omega}_{D}=\{-80 \mathbf{k}\} \ \mathrm{rad} / \mathrm{s}\) prior to application of the torque.