Answer to Question #25175 in Trigonometry for Alec Barger

Question

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?

Answer 1

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