×
Log in to StudySoup
Get Full Access to Physics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Physics - Textbook Survival Guide

CALC On a compact disc (CD), music is coded in a pat-tern

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 101CP Chapter 9

University Physics | 13th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

4 5 1 414 Reviews
27
1
Problem 101CP

CALC? On a compact disc (CD), music is coded in a pat-tern of tiny pits arranged in a track that spirals outward toward the rim of the disc. As the disc spins inside a CD player, the track is scanned at a constant ?linear? speed of v = 1.25m/s. Because the radius of the track varies as it spirals outward, the angular speed of the disc must change as the CD is played. (See Exercise 9.20.) Let’s see what angular acceleration is required to keep v constant. The equation of a spiral is r(?) = r0 + ??, where r0 is the radius of the spiral at ? = 0 and ? is a constant. On a CD, r0 is the inner radius of the spiral track. If we take the rotation direction of the CD to be positive, ? must be positive so that r increases as the disc turns and ? increases. (a) When the disc rotates through a small angle d?, the distance scanned along the track is ds = rd?. Using the above expression for r(?), integrate ds to find the total distance s scanned along the track as a function of the total angle ? through which the disc has rotated. (b) Since the track is scanned at a constant linear speed v, the distance s found in part (a) is equal to vt. Use this to find ? as a function of time. There will be two solutions for ?; choose the positive one, and explain why this is the solution to choose. (c) Use your expression for ?(t) to find the angular velocity wz and the angular acceleration ?z as functions of time. Is ?z constant? (d) On a CD, the inner radius of the track is 25.0 mm, the track radius increases by 1.55 µm per revolution, and the playing time is 74.0 min. Find r0, ?, and the total number of revolutions made during the playing time. (e) Using your results from parts (c) and (d), make graphs of wz (in rad/s) versus t and ?z (in rad/s2) versus t between t = 0 and t = 74.0 min. 9.20. Compact Disc.? A compact disc (CD) stores music in a coded pattern of tiny pits 10-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and 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 ?linear? speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum- duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.

Step-by-Step Solution:
Step 1 of 3

317 10/11/2016 Two types of Ganglion Cells Parasol Ganglion Cells Midget Ganglion Cells Larger Cells Smaller Cells Larger Receptive Fields Smaller Receptive Fields Found in Peripheral Retina Concentrated...

Step 2 of 3

Chapter 9, Problem 101CP is Solved
Step 3 of 3

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

The full step-by-step solution to problem: 101CP from chapter: 9 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. The answer to “CALC? On a compact disc (CD), music is coded in a pat-tern of tiny pits arranged in a track that spirals outward toward the rim of the disc. As the disc spins inside a CD player, the track is scanned at a constant ?linear? speed of v = 1.25m/s. Because the radius of the track varies as it spirals outward, the angular speed of the disc must change as the CD is played. (See Exercise 9.20.) Let’s see what angular acceleration is required to keep v constant. The equation of a spiral is r(?) = r0 + ??, where r0 is the radius of the spiral at ? = 0 and ? is a constant. On a CD, r0 is the inner radius of the spiral track. If we take the rotation direction of the CD to be positive, ? must be positive so that r increases as the disc turns and ? increases. (a) When the disc rotates through a small angle d?, the distance scanned along the track is ds = rd?. Using the above expression for r(?), integrate ds to find the total distance s scanned along the track as a function of the total angle ? through which the disc has rotated. (b) Since the track is scanned at a constant linear speed v, the distance s found in part (a) is equal to vt. Use this to find ? as a function of time. There will be two solutions for ?; choose the positive one, and explain why this is the solution to choose. (c) Use your expression for ?(t) to find the angular velocity wz and the angular acceleration ?z as functions of time. Is ?z constant? (d) On a CD, the inner radius of the track is 25.0 mm, the track radius increases by 1.55 µm per revolution, and the playing time is 74.0 min. Find r0, ?, and the total number of revolutions made during the playing time. (e) Using your results from parts (c) and (d), make graphs of wz (in rad/s) versus t and ?z (in rad/s2) versus t between t = 0 and t = 74.0 min. 9.20. Compact Disc.? A compact disc (CD) stores music in a coded pattern of tiny pits 10-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and 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 ?linear? speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum- duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.” is broken down into a number of easy to follow steps, and 513 words. Since the solution to 101CP from 9 chapter was answered, more than 444 students have viewed the full step-by-step answer. This full solution covers the following key subjects: track, disc, constant, angular, scanned. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460.

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

CALC On a compact disc (CD), music is coded in a pat-tern

×
Log in to StudySoup
Get Full Access to Physics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Physics - Textbook Survival Guide
×
Reset your password