Answer to Question #25175 in Trigonometry for Alec Barger

Question #25175
Data stored on a CD is read from inner radius to outer radius. The nominal inner radius of readable recording is 25 mm and usable recording ends at a radius of 59 mm. On a particular player, ω = 66.0 (radians/sec). (a) What is the linear speed under the optical pick-up at the inner radius? (b) What is the linear speed under the optical pick-up at the outer radius? (c) Compare the two linear speeds and make a rough rule about speeds at the inner and outer radii?
1
Expert's answer
2013-02-27T05:00:06-0500
ω*R = v
ω - angular speed
v - linear speed
R - radius
a) v_in = R_in * ω =25mm*66rad/sec = 1650 mm/sec = 1.65 m/sec
R_in - the inner radius
b) v_out = R_out * ω = 59mm*66rad/s= 3894 mm/sec = 3.894 m/sec
R_out - the outer radius
c) v_in/v_out = ( R_in* ω )/ (R_out * ω) = R_in/R_out =25/59 = 0.424

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