Question

Unlike record players which rotate at a constant angular velocity, the CD-ROM driver in a CD player rotates the CD at different angular velocities so that the optical head maintains a constant tangential velocity relative to the CD. Assume the CD has a diameter of 0.120 m and that the CD needs to move at a tangential velocity of 1.26 m/s relative to the optical head so the data (music) can be read correctly.a) What is the angular velocity when the CD-ROM is reading data at the outer edge of the CD? Give the answer in rpm and rad/s.b) At the inner edge of the CD, the CD-ROM rotates at 500 rpm. How far from the center of the CD is the inner edge (vtangential = 1.26 m/s)?c) What is the centripetal (radial) acceleration at the outer edge of the CD?d) What is the rotational frequency (f) of the CD when it is reading data at its outer edge?

Answer 1

Answer:

A. 21 rad/s

B. 200.5 rpm

C. 26.46 rad/s2

D. 0.299 Hz

Explanation:

Parameters given are:

Tangential velocity,v = 1.26m/s

Diameter (outer edge) = 0.120m

Outer edge radius, ro = 0.12/2

= 0.06m

A. Calculate Angular velocity

Angular velocity, w = v/r

= v/ro

= 1.26/0.06 = 21 rad/s

In rpm,

2pi/60 rad/s = 1 rpm

1 rad/s = 60/2pi rpm

Sp, 21 rad/s = 60 * 21/2pi rpm

= 200.5 rpm

B. Calculate the inner edge radius, ri given w = 500 rpm

Converting rpm to rad/s,

= 2pi/60 * 500 rad/s

= 52.34 rad/s

ri = v/w

= 1.26/ 52.36

= 0.024m

C. Calculating centripetal acceleration, a from the outer edge, ro

a = v2/r = w2r

= (1.26)2/0.06

= 26.46 rad/s

D. Calculate the frequency, f of the outer edge angular velocity, w = 21 rad/s

f = 2pi/w

= 2pi/21

= 0.299 Hz (or per second)