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?

Make sure to display the symbolic formula before plugging in the data. Please write vertically so I can understand your solution steps. Use rotational kinematics since the acceleration is non-zero.

Explanation / Answer

a)angular acceleration of the disc = 31.4/t =31.4/0.892 rad/sec^2 = 35.2rad/sec^2 b) angle rotated = v^2/2*angular acceleration = 31.4^2/2*35.2 = 14rad = 2.23 rotations c) v= rw, so speed = 4.45*31.4 = 139.73cm/sec = 1.397 m/s

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