A radar dish of radius 2.0m repeatedly sweeps horizontally from left to right through an angle of 150∘ and then returns through the same angle to its starting position. This to-and-fro motion constitutes one complete cycle. During a test run the dish performs 40 such cycles.
(i) Calculate the angular displacement, in radians, for a single sweep in one direction.
(ii) Determine the total angular displacement (in magnitude) executed by the dish during the entire test run.
(iii) Find the total length of the path traced by a point located at the rim of the dish during the 40 cycles.