Question

o read information, a CD player adjusts the rotation of the CD so that the player's readout laser moves along the spiral path at a constant speed of about 1.2 m/s. Estimate the maximum playing time of such a CD.

Express your answer to two significant figures and include the appropriat

Answer 1

From the data given  

diameter of the CD = 12 cm = 0.12 m

initial radius where the laser starts is r1 = 2.5 cm and

final radius is r2 = 5.8 cm

and the space between the centers of neighbouring spiral windings is d = 1.6*10^-6 m

the area covered is A = pi(r2^2-r1^2)

A = pi(0.058^2-0.025^2) m^2

and the toal length is l = A/d

l = pi(0.058^2-0.025^2) / (1.6*10^-6) m = 5378 m

given the velocity is v = 1.2 m/s

time taken is t = l/v = 5378 /1.2 s = 4481.67 s

t =4481.67 /60 min

t = 74.6945 min

t = 1.245 hr