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 1.6μm(=1.6×10−6m). Part 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.]

Answer 1

Answer:

total length of the spiral is L is  5378.01 m

Explanation:

Given data:

Inner radius R1=2.5 cm

and outer radius R2= 5.8 cm.

the width of spiral winding  is (d) =1.6 \mu m =  1.6x 10^{-6} m

the total length of the spiral is L is given as

$= \frac{(Area\ of\ the\ spiraing\ portion\ on\ the\ disk)}{d}$

$=\frac{\pi *(R_2)^2 - \pi*(R_1)^2}{d}$

$=\frac{\pi *(0.058)^2 - \pi*(0.025)^2}{1.6*10^{-6}}$

= 5378.01 m