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. (a) Assuming the acceleration is constant, find the total angular displacement of the disc as it plays from the outside at 2.10 cm to the inside at 6.10 cm. (b) Find the total length of the track.

A full- length recording lasts for 74 min, 33 s ,

t=74 min33 sec =4473 s
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
φ=εt²/2=0.0085•4473²/2=85032.8 rad
L=v•t=1.22•4473=5457.06 m

I assume that you have inside and outside reversed and I assume that it is the angular acceleration that is constant.

alpha = angular acceleration = dw/dt = constant

r outside = .061 m
r inside = .021 m
I am assuming you mean radius and not diameter. If you copied this question from a book they really messed it up.

.60 mm = .6 * 10*-3 m = 6 * 10^-4 meters/bit

v = w r = 1.22 m/s
v is constant so w =1.22/r

Initial angular velocity wi at outside:
wi = 1.22/.061 = 20 radians/second
Final angular velocity wf at inside:
wf = 1.22/.021 = 58 radians/second

angular acceleration alpha = (58-20)/time

Now to find the time I need how many total bits are on the track. (unless the time was given)

Once you find the angular acceleration, alpha, and knowing the time, integrate to find the total angular displacement

theta = wi t + (1/2) alpha t^2

okay I would just skip it I'm in 7th grade and that looks hard

To solve this problem, we need to break it down into two parts:

(a) The total angular displacement of the disc as it plays from the outside at 2.10 cm to the inside at 6.10 cm.

First, let's convert the given values into meters:
- Outside radius (Rout) = 2.10 cm = 0.0210 m
- Inside radius (Rin) = 6.10 cm = 0.0610 m

Next, we can find the circumference of the disc at both the inside and outside:
- Circumference at outside edge = 2πRout
- Circumference at inside edge = 2πRin

Then, we can subtract the two circumferences to find the difference:
- Difference in circumference = Circumference at inside edge - Circumference at outside edge

Now, we can divide the difference in circumference by the length of one bit (0.60 mm = 0.0006 m) to find the total number of bits on the track:
- Total number of bits = Difference in circumference / Length of one bit

Finally, we can calculate the angular displacement using the formula:
- Angular displacement = Total number of bits * length of one bit / Circumference at inside edge

(b) The total length of the track.

To find the total length of the track, we can calculate the length between the two circumferences:
- Length between the two circumferences = Difference in circumference

Then, we can calculate the total length of the track (L) by multiplying the length between circumferences with the total number of bits:
- Total length of the track = Length between the two circumferences * Total number of bits

By following these steps, we can find the solutions to both parts of the problem.