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.\" 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-third 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 6.61 seconds, how many revolutions would the Armin van Buuren record sweep?

Answer 1

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 3/4). Therefore, they match at (3/4)(33.3) = 24.98 rpm.

The average rotational speed of record A during this interval is 7/8 of 33.3 rpm (average of 1 x 33.3 and 3/4 x 33.3 = ((1 + 3/4)/2) x 33.3.) = 29.14.

Divide that number by 60 to get the number of revolutions per second, then multiply by 6.61 second = 3.21 rev