On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are e

Question

On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are encoded sequentially along an outward spiraling path. The spiral starts at radius R1 = 2.7 cm and winds its way out to radius R2 = 5.9 cm . To read the digital information, a CD player rotates the CD so that the player's readout laser scans along the spiral's sequence of bits at a constant linear speed of 1.22 m/s . Thus the player must accurately adjust the rotational frequency f of the CD as the laser moves outward.

Determine the values for f (in units of rpm) when the laser is located at R1.

Express your answer using two significant figures.

Determine the values for f (in units of rpm) when the laser is located at R2

Express your answer using two significant figures.

Explanation / Answer

use the relatin between V = r W

so W = V/r

where V is velocity

r is raidus

so

also 1 RPM = 2pi/60

so

W for R1 = 1.22/(0.027) * 60/(2*3.14)

W = 431.7 rad/s for R1

---------------------------------

use the relatin between V = r W

so W = V/r

where V is velocity

r is raidus

so

also 1 RPM = 2pi/60

so

W for R1 = 1.22/(0.059) * 60/(2*3.14)

W = 197.56 rad/s for R2

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