Question
Estimate the length of the spiral carrying pits and lands on an ordinary CD of diameter $12 \mathrm{cm} .$ Assume that adjacent parts of the spiral are $1600 \mathrm{nm}$ apart. Explain your method, listing the assumptions you have made.
Step 1
A CD (compact disc) is typically a circular disc. The data on a CD is stored in a single continuous spiral track of pits and lands that starts near the center and moves outward. The diameter of the CD is given as 12 cm. Show more…
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(II) Digital bits on a 12.0 -cm diameter audio CD are encoded along an outward spiraling path that starts at radius $R_{1}=2.5 \mathrm{cm}$ and finishes at radius $R_{2}=5.8 \mathrm{cm}$ . The distance between the centers of neighboring spiralwindings is 1.6$\mu \mathrm{m}\left(=1.6 \times 10^{-6} \mathrm{m}\right)$ . (a) Determine the unwinding the spiral into a straight path of width 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 $\mathrm{m} / \mathrm{s}$ . Estimate the maximum playing time of such a CD.
Consider again the DVD in Problem $60 .$ As was explained in Example 8.2 , the data on the DVD are encoded in a long spiral "track," where the spacing between each turn of the track is $0.74 \mu \mathrm{m}$ and the inner and outer radii of the program area are about $25 \mathrm{mm}$ and $58 \mathrm{mm},$ respectively. Estimate the length of this spiral.
Rotational Motion
Rotational Dynamics
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