Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_164

6/164 The gear train shown starts from rest and reaches an output speed of \(\omega_C = 240 \text{ rev/min}\) in \(2.25 \text{ s}\). Rotation of the train is resisted by a constant \(150 \text{ N}\cdot\text{m}\) moment at the output gear \(C\). Determine the required input power to the \(86\%\)-efficient motor at \(A\) just before the final speed is reached. The gears have masses \(m_A = 6 \text{ kg}\), \(m_B = 10 \text{ kg}\), and \(m_C = 24 \text{ kg}\), pitch diameters \(d_A = 120 \text{ mm}\), \(d_B = 160 \text{ mm}\), and \(d_C = 240 \text{ mm}\), and centroidal radii of gyration \(k_A = 48 \text{ mm}\), \(k_B = 64 \text{ mm}\), and \(k_C = 96 \text{ mm}\).