13. -11 points SerCP11 7.P050 My Notes Ask Your Teacher A digital audio compact

Question

13. -11 points SerCP11 7.P050 My Notes Ask Your Teacher 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 0.6 m of the track. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.35 m/s. (a) Find the required angular speed at the beginning of the recording where the spiral has a radius of 2.30 cm. (Enter your answer to at least one decimal place.) rad/s (b) Find the required angular speed at the end of the recording, where the spiral has a radius of 4.70 cm. (Enter your answer to at least one decimal place.) rad/s (c) A full-length recording lasts for 60 min, 33 s. Find the average angular acceleration of the disc. rad/s2 (d) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays rad (e) Find the total length of the track. km Need Help? Read It Watch It

Explanation / Answer

a) angular speed w = v/r

wi = 1.35/2.3*10^-2

wi = 58.69 rad/s

b) wf = 1.35/4.7*10^-2 = 28.72 rad/s

c) angular acceleration = wf-wi/t = 28.72-58.69/(60*60+33) = -0.0082 rad/s^2

d) angular displacement = wf^2-wi^2/2**angular acceleration)

angular displacement = 28.72^2-58.69^2/2(-0.0082) = 159736.3 rad

e) length x = v*t = 1.35*3633 = 4904.55 m

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