Question

A digital audio compact disc carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.60 mm of the track. A CD player turns the disc to carry the track counter-clockwise above a lens at a constant speed of 1.22 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.10cm. (b) at the end of the recording, where the spiral has a radius of 6.10 cm. (c) A full- length recording lasts for 74 min, 33 s. Find the average angular acceleration of the disc as it spins from the outside at 2.10 cm to the inside at 6.10 cm.

Answer 1

t=74 min33 sec =4473 sá

ω1=v/R1 =1.22/0.021 = 58.1 rad/s
ω2=v/R2 =1.22/0.061 = 20 rad/s

ε= (ω2- ω1)/t =(20-58.1)/ 4473=-0.0085 rad/s²