Problem

The top of the Space Needle in Seattle, Washington, hosts a revolving restaurant that goes...

The top of the Space Needle in Seattle, Washington, hosts a revolving restaurant that goes through one full revolution every 47 min under the action of a motor with a power output of 1.5 hp. The portion of the restaurant that rotates is a ring-shaped turntable with internal and external radii ri = 33.3 ft and ro = 47.3 ft, respectively, and approximate weight W = 125 tons (1 ton = 2000 lb). Use the given values of power output and angular speed to estimate the torque M that the engine provides. Then, assuming that the motor can provide a constant torque equal to M, neglecting all friction, and modeling the turntable as a uniform body, determine the time ts that it takes to spin up the revolving restaurant from rest to its working angular speed.