Chapter 2, Problem 13P

(II) Digital bits on a 12.0-cm diameter audio CD are encoded along an outward spiraling path that starts at radius R₁ = 2.5 cm and finishes at radius R₂ = 5.8 cm. The distance between the centers of neighboring spiral-windings is 1.6 µm (= 1.6 × 10^‒6m). (a) Determine the total length of the spiraling path. [Hint: Imagine “unwinding” the spiral into a straight path of width 1.6µm, and note that the original spiral and the straight path both occupy the same area.] (b) To read information, a CD player adjusts the rotation of the CD so that the player’s readout laser moves along the spiral path at a constant speed of 1.25 m/s. Estimate the maximum playing time of such a CD.