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=6.0cm=0.060m; when data are being read, it spins at 7200 rev/min. What is the CD's angular velocity in radians per second? How much time is required for it to rotate through 90? If it starts from rest and reaches full speed in 4.0 s, what is its average angular acceleration? an old-fashioned vinyl record is designed to turn at 33 rev/min. Find the average angular velocity. 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.

Explanation / Answer

Here ,

angular speed pf CD = 7200 rev/min

angular speed pf CD = 7200 * 2pi/60

angular speed pf CD = 753.8 rad/s

the angular speed of CD is 753.8 rad/s

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time taken = angle/w

time taken = (90 * 3.141/180)/753.8

time taken = 0.0021 s

the time taken to rotate 90 degree is 0.0021 s

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let the angular acceleration is a

w = 0.5 * a * t^2

753.8 = 0.5 * a * 4^2

a = 94.22 rad/s^2

the angular acceleration of the CD is 94.22 rad/s^2

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angular speed , w = 33 rev/min

w = 3.455 rad/s

angular velocity is 3.455 rad/s

for the angle velocity is a

3.455^2 = 2 * a * 4 * 2 *3.141

a = - 0.237 rad/s^3

the angular acceleration is - 0.237 rad/s^2

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