The CD-ROM drive in a computer accelerates a disk from rest to its full speed of

Question

The CD-ROM drive in a computer accelerates a disk from rest to its full speed of 20000 revolutions per minute; it does so uniformly over 5 seconds. The disk is 6 cm in radius.

(e) After four seconds, what is the tangential velocity of a point along the edge of the disk?

(f) After four seconds, what is the angular velocity of a point along the edge of the disk?

(g) After four seconds, what is the tangential acceleration of a point along the edge?

(h) After four seconds, what is the radial acceleration of a point along the edge? Speculate on the engineering consequences of this figure; how large is it compared to other accelerations you know?

Explanation / Answer

here,

final speed , w = 20000 rev/min = 2093.3 rad/s

time taken , t = 5 s

radius , r =0.06 m

let the angular accelration be alpha

w = w0 + alpha * t

2093.3 = 0 + alpha * 6

alpha = 348.9 rad/s

e)

at t1 = 4 s,

the angular velocity , w1 = 0 + alpha * t1 = 1395.6 rad/s

the tangential velocity , v1 = w1 * r = 83.7 m/s

f)

at t1 = 4 s,

the angular velocity , w1 = 0 + alpha * t1 = 1395.6 rad/s

g)

the tangential accelration , at = r * alpha = 20.88 m/s^2

h)

the radial accelration , alpha = 348 rad/s^2

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