   Chapter 7, Problem 50AP

Chapter
Section
Textbook Problem

A digital audio compact disc (CD) carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.6 μm of the track. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.30 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.30 cm, and (b) at the end of the recording, where the spiral has a radius of 5.80 cm. (c) A full-length recording lasts for 74 min, 33 s. Find the average angular acceleration of the disc, (d) Assuming the acceleration is constant, find the total angular displacement of the disc as it plays, (e) Find the total length of the track.

(a)

To determine
The angular speed of the disc at the beginning of the recording.

Explanation

Given Info: The radius of the spiral at the beginning of the recording is 2.30cm and CD player turns the disc above the lens at a constant speed of 1.30m/s .

Explanation:

Formula to calculate the angular speed of the disc is,

ωi=vri

• ri is the radius of the spiral
• v is the constant speed of CD disc

Substitute 1.30m/s for v and 2

(b)

To determine
The angular speed of the disc at the end of the recording.

(c)

To determine
The average angular acceleration of the disc.

(d)

To determine
The total angular displacement of the disc if the acceleration is constant.

(e)

To determine
The total length of the track.

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