A digital audio compact disc carries data, each bit of which occupies 0.6 um alo

Question

A digital audio compact disc carries data, each bit of which occupies 0.6 um along a continuous spiral track from the inner circumference of the disc to the outside edge. A CD player turns the disc to carry the track counterclockwise above a lens at nstant peed of m/ (a) Find the required angular speed at the beginning of the recording, where the spiral has a radius of 2.10 cm. 52 (b) Find the angular speed at the end of the recording, where the spiral has a radius of 5.70 cm. 19.3 (c) A full-length recording lasts for 74 min 33 s. Find the average angular acceleration of the disc. rad/s rad/s (d) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays. rad (e) Find the total length of the track.

Explanation / Answer

v = r

v = 1.10 m/s constant speed

a)

inner radius = 2.10 cm = .0210 m

= v/r = 1.10/ .0210 = 52.38 rad/s

b) angular speed at the end of the recording, where the spiral has a radius of 5.70 cm.

= v/r = 1.10/0.0570 = 19.3 rad/s

c)

Average Angular Acceleration

• The average angular acceleration of an

object is defined as the ratio of the change in the angular speed to the time it takes for the object to undergo the change:

= / t

Unit: rad/s²

total time = 74 min 33 s = 74x60 + 33 = 4473 s

= (19.3 – 52.38)/4473 = -7.4*10^-3 rad/s²

d) since is constant average = (19.3 + 52.38)/2 = 35.84 rad/s

t = 4473 s

= total angular displacement

=> = /t => = x t = 35.84*4473 = 160312.32 radians

e) the total length of the track

distance = speed x time = 1.10 m/s x 4473 = 4920.3m or 4.9203 km

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