A compact disk (CD) in a computer rotates from rest up to an angular speed of 31

Question

A compact disk (CD) in a computer rotates from rest up to an angular speed of 31.4 rad/sec in 0.892 sec.
a) What is the angular acceleration of the disc? b) How many rotations does it make while coming up to speed? c) If the radius of the CD is 4.45 cm, what would be the speed of a microbe riding on the rim of the CD? d) What is the magnitude of the tangential acceleration at this time? e) What is the angular speed and angular displacement of the CD 0.3 seconds after it begins to rotate? A compact disk (CD) in a computer rotates from rest up to an angular speed of 31.4 rad/sec in 0.892 sec.
a) What is the angular acceleration of the disc? b) How many rotations does it make while coming up to speed? c) If the radius of the CD is 4.45 cm, what would be the speed of a microbe riding on the rim of the CD? d) What is the magnitude of the tangential acceleration at this time? e) What is the angular speed and angular displacement of the CD 0.3 seconds after it begins to rotate? A compact disk (CD) in a computer rotates from rest up to an angular speed of 31.4 rad/sec in 0.892 sec.
a) What is the angular acceleration of the disc? b) How many rotations does it make while coming up to speed? c) If the radius of the CD is 4.45 cm, what would be the speed of a microbe riding on the rim of the CD? d) What is the magnitude of the tangential acceleration at this time? e) What is the angular speed and angular displacement of the CD 0.3 seconds after it begins to rotate?

Explanation / Answer

a)

Since it starts from rest ,initial angular speed is zero i.e Wo=0

from W=Wo+alpha*t

31.4=0+alpha*0.892

alpha=35.2 rad/sec2

b)

from

theta =Wot+(1/2)*alpha*t2

theta=0+(1/2)*35.2*0.8922

theta =14 rad

in revolutions

theta =14/2pi=2.23 revolutions

c)

speed

V=rW=0.0445*31.4=1.4 m/s

d)

Tangential acceleration

at=r*alpha=0.0445*35.2

at=1.57 m/s2

e)

at t=0.3 s

W=0+35.2*0.2=10.56 rad/sec

theta =0+(1/2)*35.2*0.32=1.584 rad

in rev

theta =1.584/2pi=0.252 rev

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