Trance music often relies on a DJ playing two records at the same time. The basi

Question

Trance music often relies on a DJ playing two records at the same time. The basic time signatures of the two Turntable A Turntable B records must match, however, otherwise the two records will play "out of synch." A DJ is playing an Armin van Buuren record on Turntable A at a typical 33.3 rpm, while a Blank & Jones record rests motionless on Turntable B. At a given time, he turns on one record and turns off the other. If the Armin van Buuren record rotationally decelerates at one-fourth the rate of rotational acceleration of the Blank & Jones record, at what rotational speed will the two turntables match when they finally "synch"? If this process took 7.63 seconds, how many revolutions would the Armin van Buuren record sweep?

Explanation / Answer

Given

Disk A’s initial velocity o = 33.3 rpm

Disk b’s initial velocity o’ = 0 rpm

Acceleration of disk B =

Acceleration of disk a = -/4

Solution

A)

Writing equations of motion for both disks. Let be the velocity obtained after time t which is in sync

= 0 - t/4

=33.3 – t/4 ……..(1)

= o’ + t

= 0 + t ……………(2)

= t = 33.3 – t/4

5t/4 = 33.3

t = 33.3 x 4 / 5 = 26.64

= 26.64 rpm

B)

= 26.64 rpm = 0.444 revolutions per second

o = 33.3 rpm = 0.555 revolutions per second

2 = o2 – (/4)

we know now = t = 0.444 rps so = 0.444 / 7.63 = 0.0582 revolutions per second per second

0.4442 = 0.5552 – (0.0582/4)

= 7.62 revolutions

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