A digital audio compact disc (CD) carries data along a continuous spiral track f

Question

A digital audio compact disc (CD) carries data along a continuous spiral track from the inner circumference of the disk to the outside edge. Each bit occupies 0.6 ?m of the track. A CD player turns the disc to carry the track counter clockwise above a lens at a constant speed of 1.30 m/s. (a) Find the angular speed at the beginning and at the end of the recording where the spiral has a radius of 2.30 cm and 5.80 cm, respectively. (b) A full-length recording lasts for 74 minutes and 33 seconds. Find the average angular acceleration of the CD. (c) Find the total length of the track

Explanation / Answer

? = v/R v = 0.90 m/s (a) R = 2.60 cm = 0.026 m, ? = 0.90/0.026 = 34.615 rad/s (b) R = 6.10 cm = 0.061 m, ? = 0.90/0.061 = 14.754 rad/s (c) ?t = 74 mn 33 s = 4473 s . .?? = 14.754 - 34.615 = -19.861 rad/s Angular acceleration: a = ??/?t = -19.861 / 4473 = -0.00444 rad/s² (d) Angular displacement: ? = -(1/2)at² = (0.00444/2)×4473² = 44,417 radian (e) Total length of the track: L = v?t = 0.90 × 4473 = 4025.7 m

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