Unlike the older vinyl records which rotated at a constant ? of 33.3 rotations p

Question

Unlike the older vinyl records which rotated at a constant ? of 33.3 rotations per minute (rpm), compact disks vary their rotation speed during the playing period. A certain CD has a diameter of 12cm and a playing time of 72.0 minutes. When the music starts, the CD is rotating at 480 rpm. At the end of the music, the CD is rotating at 218.0 rpm. 1) What is the final rotational velocity of a point on the very outer edge of the disk? ?f1 = 2) What is the final rotational velocity of a point that is half way between the center of the disk and the outer edge? ?f2 = 3) What is the final tangetial speed of a point on the very outer edge of the disk? 4) What is the final tangential speed of a point half way between the center of the disk and its outer edge? vT2 = 5) What is the magnitude of the average angular acceleration of the disk during this playing period? ?AVG =

Explanation / Answer

1) What is the final rotational velocity of a point on the very outer edge of the disk? ?

1 = (2*3.1416*218.0/60) = 22.82896 22.8 rad/s

2) What is the final rotational velocity of a point that is half way between the center of the disk and the outer edge? ?

2 = (2*3.1416*218.0/60) = 22.82896 22.8 rad/s

3) What is the final tangetial speed of a point on the very outer edge of the disk?

v1 = 0.12 * (2*3.1416*218.0/60) = 2.7394752 2.74 m/s

4) What is the final tangential speed of a point half way between the center of the disk and its outer edge?

vT2 = 0.12/2 * (2*3.1416*218.0/60) = 1.3697376 1.37 rad/s

5) What is the magnitude of the average angular acceleration of the disk during this playing period? ?

f = (2*3.1416*218.0/60) = 22.82896 rad/s

i = (2*3.1416*480/60) = 50.2656 rad/s

AVG = (22.82896 - 50.2656)/(72.0*60) = -6.35e-3 rad/s2

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