Question

6. 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.

(a) Is it correct to write ? = 4000rev · min?1 · s?1? Explain.

(b) What is the maximum angular velocity in our conventional units of radians per

second?

(c) What is its angular acceleration?

(d) How many times does it spin during this interval?

(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?

Answer 1

a) Using the angular acceleration relation, we have

The answer for alpha is same, but in physics we prefer same units for at least a single variable, here the time has two units minutes and seconds. So, it is not correct to write it this way.

b) Maximum angular velocity is 20,000 revolutions per minute.

In one revolution, the angle traced is 2*pi radians, and in 1 minute we have 60 seconds. Thus,

c) Doing angular acceleration in proper units, we have

d) Calculating the angle traced by disc in 5 seconds,

Now, corresponding to 2*pi = 6.28 radians, one revolution is made. Therefore, corresponding to above angle, number of revolutions are

These many times, the disc spun.

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