A circular amusement-park ride consists of a rigid, flat platform of rotational inertia 1.5×103kgm2 (about its central vertical axis) and a ring of seats attached around the edge. When fully loaded with passengers, the seats and riders together contribute an additional rotational inertia of 2.5×103kgm2 about the same axis. A motor applies a constant net torque of 4.0×103Nm to spin the ride up from rest. Assume frictional torques are negligible.
(a) Calculate the magnitude of the angular acceleration of the ride when it is fully loaded.
(b) The operator now removes several seat sections, reducing the passenger-ring rotational inertia by 30 percent while leaving the platform unchanged. If the same motor torque is applied to the partially loaded ride, determine the new angular acceleration.
(c) Suppose the ride must reach an angular speed of 1.0rads−1 before a light turns green to load the next group of passengers. Compare the spin-up time required for the fully loaded and partially loaded configurations. Provide quantitative results and explain the difference.
(d) Discuss one safety consideration the operator should keep in mind when the ride accelerates more rapidly with fewer passengers. Your answer should reference physical quantities involved in rotational motion.