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 sync." DJ Bob is playing a Deadmau5 record on Turntable A at a typical 33.3 rpm, while a Wolfgang Gartner record rests motionless on Turntable B. At a given time, he turns on one record and turns off the other. If the Deadmau5 record rotationally decelerates at one-fifth the rate of rotational acceleration of the Wolfgang Gartner 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 Deadmau5 record sweep?

Explanation / Answer

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

Therefore, they match at 5/6(33.3) rpm. The average rotational speed of record A during this interval is 11/12 of 33.3 rpm.

(average of 1 x 33.3 and 5/6 x 33.3 = ((1 + 5/6)/2) x 33.3.) = 30.525

Divide that number by 60 to get the number of revolutions per secondthen

= 30.525 / 60 = 0.50875 rpm

multiply by 7.63 seconds

= 0.50875 x 7.63 = 3.88 rev.

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