# Answer on Trigonometry Question 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?

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?

Expert's answer

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

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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