Digital bits on a 12.0-cm diameter audio CD are encoded along an outward spirali

Question

Digital bits on a 12.0-cm diameter audio CD are encoded along an outward spiraling path that starts at radius R1=2.5cm and finishes at radius R2=5.8cm. The distance between the centers of neighboring spiral-windings is 1.6m(=1.6×106m).

Part A Determine the total length of the spiraling path. [Hint: Imagine "unwinding" the spiral into a straight path of width 1.6m, and note that the original spiral and the straight path both occupy the same area.] Express your answer to two significant figures and include the appropriate units.

Part 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 about 1.2 m/s. Estimate the maximum playing time of such a CD.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Ans: Inner radius r1=2.5 cm and outer radius r2= 5.8 cm.the width when it is straight is (d) = 1.6x 10-6 m

a)So the length of the spiral is L= (Area of the spiraing portion on the disk)/d =(pi *(R2)^2 - pi*(R1)^2)/d = 5378 m

b)the maximun plating time t = L/v ; Where v=1.2 m/sec hence, t =4481.7 sec

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