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**1. Homework Statement**

A digital audio compact disc carries data, with each bit occupying 0.6 (mu)m, along a continuous spiral track from the inner circumference of the disc to the outside edge. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.3 m/s. Find the required angular speed a) at the beginning of the recording, where the spiral has a radius of 2.3 cm and b) at the end of the recording, where the spiral has a radius of 5.8 cm c) A full-length recording lasts for 74 min 33s. Find the average angular acceleration of the disc. d) Assuming that the accleration is constant, find the total angular displacement of the disc as it plays. e) Find the total length of the track.

**2. Homework Equations**

v=rw

(alpha)=(omega)/time

w=w_o+(alpha)t

**3. The Attempt at a Solution**

For a) I converted the radius of 2.3 cm to meters: 0.023 meters

I used the equation: v=rw to solve for the angular speed (w):

1.3m/s=(0.023m)W --> W=56.52 rad/s

b) same method as a): v=rW --> 1.3m/s=(0.058m)W --> W=22.4 rad/s

c) I used the equation: W=W_o+(alpha)t

t=74 min 33s or 4473s

I used the answers for a) and b) for the initial/final angular speeds. Is this correctly done? 22.4 rad/s=56.52 rad/s+(alpha)(4473s)

Solving for (alpha) I got (alpha)= -7.628x10^-3

I'm a little ambiguous about the answers I've obtained for a) and b). I thought that the angular speed for a larger radius should be larger than the circumference with the smaller radius. Does this only apply to the tangential speed/velocity? I remember reading somewhere that the outside of the circular rotational motion moves faster than the inside if they were both on the same reference line. Are my attempts correct so far? How can the angular accleration(alpha) equal such a small negative number? I don't really understand how the angular velocities and accelerations work because they are related to theta =/ Can someone please explain it to me? Thanks!