Let\'s begin with the angular acceleration of a compact disk (CD). To play music

Question

Let's begin with the angular acceleration of a compact disk (CD). To play music the CD must rotate at high speed while a laser reads data encoded in a spiral pattern on the disk. The disc has radius R = 6.0 cm = 0.060 m: when data are being read. it spins at 7200 rev/min. What is the CD's angular velocity w in radians per second? How much time is required for it to rotate through 90 degree? If it starts from rest and reaches full speed in 4.0 s. what is its average angular acceleration? Part B - Practice Problem: Find the angular acceleration of the record if it spins through four full rotations before coming to a stop when the record player is turned off. Express your answer in radians second squared to two significant figures.

Explanation / Answer

here,

radius , r = 6 cm

r = 0.06 m

(a)

angular velocity , w = 7200 rev/m

w = 7200 * 6.28 / 60

w = 753.6 rad/s

the angular velocity is 753.6 rad/s

(b)

let the time to rotate through 90 degree be t

theta = 90 degree

theta = pi/2 rad

t = theta/w

t = pi / ( 2 * 753.6)

t = 2.08 * 10^-3 s

or t = 2.08 ms

(c)

let the angular accelrationn be a

t = 4 s

using first equation of motion

wf = w0 + a*t

753.6 = 0 + a * 4

a = 188.4 rad/s^2

the angular accelration is 188.4 rad/s^2

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