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.

A. If the Deadmau5 record rotationally decelerates at one-third the rate of rotational acceleration of the Wolfgang Gartner record, at what rotational speed will the two turntables match when they finally "synch"?

B. If this process took 4.57 seconds, how many revolutions would the Deadmau5 record sweep?

Explanation / Answer

Here, let rotational speed of Deadmau5 be om1 (subscritp denoting initial or final), rotational acceleration be al1.

Then, the same for Garter record are om2 and al2 respectively.

Now, in this question, om1initial= 33.3 rpm, al1= -a (deleceration)

om2initial = 0 rpm, and al2 = 3*a

A.)

So, for om2final =om1final at some time t,

om1final - om1initial = -a*t => om1final - 33.3= -a*t

om2final - om2initial = 3*a*t => om2final -0= 3*a*t-----(i)

om2final =om1final => 33.3 - a*t = 3*a*t

=> a*t = 33.3/4

So, om2final =om1final = 3*a*t = 3*33.3/4 rpm = 24.975 rpm (i)

B. Given, t= 4.57 s = 4.57/60 min

Now, a*t = 33.3/4 rpm => a = 33.3/4 * (60/4.57) rev/ min2 = 109.3 rev/ min2

Now, om12final - om12initial = 2*-a*rev, where rev is total no of revolutions (units in rpm and minutes)

=> 24.9752 - 33.32 = 2* (-109.3)* rev

=>rev = (24.9752 - 33.32 )/(2* (-109.3)) = 2.22 revolutions

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