A person stands at the center of a light, frictionless turntable holding a 3.0m-long lightweight rod horizontally. Identical 1.0kg masses are attached to each end of the rod. The person and platform together have a moment of inertia of 2.8kgm2 about the central vertical axis. Initially the system rotates at 2.0rads−1. A built-in motor reels both masses smoothly and simultaneously toward the axis, bringing them to a radius of 0.40m in 1.5s. Assume no external torques act.
(a) Derive an expression for the angular speed ω(t) of the system while the masses move inward at a constant radial speed.
(b) Calculate the final angular speed once the masses reach 0.40m.
(c) Using your result from part (b), determine the average mechanical power delivered by the motor during the reeling process.
(d) Discuss qualitatively how your answers would be affected if a small, constant external friction torque acted on the platform during the 1.5s interval.