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-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 4.57 seconds, how many revolutions would the Armin van Buuren record sweep?

Explanation / Answer

Let a be the angular acceleration and w the angular frequency:

w1 = w0 - a t     speed of first record at match

w2 = 3 a * t     speed of second record at match

3 a * t = w0 - a * t     when the two records match

a = w0 / (4 * t)

w0 = 33.3 * 2 * pi / 60 = 3.49 / sec     initial angular speed

a = 3.49 / (4 * 4.57) = .191    angular deceleration

3 * .191 * 4.57 = 2.62 / sec      angular speed at match

theta = w0 t - 1/2 a t^2

theta = 3.49 * 4.57 - 1/2 * .191 * 4.57^2 = 14 rad

14 rad / (2 * pi) = 2.22 rev

Check: w0 - a t = 3.49 - .191 * 4.57 = 2.62   speed of first record at match

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.