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 records must match, however, otherwise the two records will play "out of synch." Turntable A Turntable B 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 33.3 rpm 0 rpm If the Armin van Buuren record rotationally decelerates at one-third the rate of rotational acceleration of the Blank & Jones record, at what rotational speed will the two turntables match when they finally "synch"? Number 24.98 rpm If this process took 3.55 seconds, how many revolutions would the Armin van Buuren record sweep? Number rev

Explanation / Answer

Since the acceleration is 3 times the deceleration, B accelerates to 3/4 of the speed while A decelerates 1/4 of the speed (from full speed down to 5/6).

Therefore, they match at:

3/4(33.3) rpm = 24.98 rpm (ans)

The average rotational speed of record A during this interval is:

average of 1 x 33.3 and 3/4 x 33.3 = ((1 + 3/4)/2) x 33.3

= 29.1375rpm

Divide that number by 60 to get the number of revolutions per second,

= 29.1375 x (1/60) = 0.485625 rps

then multiply by 6.61 seconds to get the answer:

= 0.485625 rps * 3.55s = 1.724 rev (ans)

Hope this helps :)

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