Need to find the answer to this please and thanks! Digital bits on a 12.0-cm dia

Question

Need to find the answer to this please and thanks!


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 1.6X10^-6 m.

Determine the total length of the spiraling path. [Hint: Imagine "unwinding" the spiral into a straight path of width , 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.

Explanation / Answer

Hi, Given the distance between neighboring spiral-windings is a = 1.6 * 10^(-6) m. For a circle of radius r, the circumference = 2 * p * r. Hence the number of spiral windings in this length = dn = 2pr/a. Hence the total number of spiral windings in the area enclosed on the CD within the range of radius r1 and r2 is given by        N = Integral(dn) within limits r1 and r2 = Integral(2pr/a) within limits r1 and r2       = (pr^2 /a) within limits r = 2.5 * 10^(-2)m to r = 5.8 * 10^(-2)m       ˜ 5375 Hope this helps you. Hope this helps you.

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