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." 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 3.55 seconds, how many revolutions would the Armin van Buuren record sweep?

Explanation / Answer

given
wBi = 33.3 rpm = 33.3*2*pi/60 = 3.485 rad/s
wAi = 0

let alfa_A and alfa_B are the accelarations.

here, alfa_A = alfa_B/3

here, final angular speeds are same.

wBf = WAf

wBi + alfa_B*t = wAi- alfa_A*t

o + alfa_B*t = 3.485 - (alfa_B/3)*t

alfa_B*t*(1 + 1/3) = 3.485

alfa_B*2.53*4/3 = 3.485

alfa_B = 2.614/2.53

alfa_B = 1.033 rad/s

so, wBf = WBi + alfa_B*t

= 0 + 1.033*2.53

= 2.614 rad/s

= 2.614*60/(2*pi)

= 24.97 rpm <<<<<<<<<<<<<<<<----------------Answer

theta_B = wBi*t + 0.5*alfa_B*t^2

= 0 + 0.5*1.033*2.53^2

= 3.3 rad

= 0.526 revoltuions <<<<<<<<<<<<<<<<----------------Answer

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