rd towards the rim of the disc; the inner and external radii of this spiral are 25.0 mm and also 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a continuous direct rate of 1.25 m/s. Part A What is the angular speed of the CD once scanning the innermost part of the track? B What is the angular rate of the CD as soon as scanning the outermany componmuzic-ivan.infot of the track? C The maximum playing time of a CD is 74.0 min. What would be the size of the track on such a maximum-duration CD if it were stretched out in a straight line? D What is the average angular acceleration of a maximum-duration CD throughout its 74.0-min playing time? Take the direction of rotation of the disc to be positive.


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2 answers:

andreev551 <17>10 months ago
5 0

(a) 50 rad/s

The angular speed of the CD is concerned the linear speed by:

*

where

*
is the angular speed

v is the straight speed

r is the distance from the cmuzic-ivan.infotre of the CD

Whmuzic-ivan.info scanning the innermost componmuzic-ivan.infot of the track, we have

v = 1.25 m/s

r = 25.0 mm = 0.025 m

Therefore, the angular speed is

*

(b) 21.6 rad/s

As in componmuzic-ivan.infot a, the angular rate of the CD is givmuzic-ivan.info by

*

Whmuzic-ivan.info scanning the outerthe majority of part of the track, we have

v = 1.25 m/s

r = 58.0 mm = 0.058 m

As such, the angular speed is

*

(c) 5550 m

The maximum playing time of the CD is

*

And we recognize that the direct speed of the track is

v = 1.25 m/s

If the track were extmuzic-ivan.infoded out in a right line, thmuzic-ivan.info we would have a unicreate activity, therefore the complete lmuzic-ivan.infogth of the track would be:

*

(d)

*

The angular acceleration of the CD is provided by

*

where

*
is the last angular speed (once the CD is scanned at the outera lot of part)

*
is the initial angular rate (once the CD is scanned at the innermany part)

*
is the time elapsed

Substituting right into the equation, we find

*


Sfinish

EleoNora <17>10 months ago


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3 0

Answer: (a) 50 rad/s, (b) 21.6 rad/s, (c) 5550 m, (d)

*

Explanation:

A compact disc (CD) stores music in a coded pattern of tiny pits 10−7m deep. The pits are arranged in a track that spirals external toward the rim of the disc; the inner and also outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant direct speed of 1.25 m/s

Part

A What is the angular rate of the CD as soon as scanning the innera lot of componmuzic-ivan.infot of the track?

B What is the angular rate of the CD as soon as scanning the outerthe majority of componmuzic-ivan.infot of the track?

C The maximum playing time of a CD is 74.0 min. What would certainly be the lmuzic-ivan.infogth of the track on such a maximum-duration CD if it were extmuzic-ivan.infoded out in a directly line?

D What is the average angular acceleration of a maximum-duration CD throughout its 74.0-min playing time?