Question 24 of 34 Map da Sapling Learning Trance music often reliles on a DJ pla

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Question 24 of 34 Map da Sapling Learning Trance music often reliles 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. Turntable A Tumtable B 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 tuns on one record and turns off the other 33.3 rpm 0 rpm 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"? Number rpm If this process took 5.59 seconds, how many revolutions would the Armin van Buuren record sweep? Number rev

Explanation / Answer

a)

in case of Armin van Buuren,

initial angular speed, w1A=33.3 rpm = 3.487 rad/sec

final anglar speed, w2A

and

in case of Blank and Jones ,

initial angular speed is w1B=0

final anglar speed is w2B

and

given,

alpa_A=1/3*alpa_B

(w1A-w2A)/t=1/3*(w2B-w1B)/t

here,

W2A=W2B

then,

(w1A-w2A)=1/3*(w2A-0)

==>

3*(W1A-W2)A=w2A

===> 3*W1A=4*W2A

==> w2A=3/4*W1A

W2A=3/4*(3.487)

w2A=2.615

b)

deceleration, alpa_A=W2A-W1A/t

=(2.615-3.487)/(5.59)

=-0.156 rad/sec^2

and

angular displacement, theta=w1A*t+1/2*alpa*t^2

=3.487*5.59-1/2*0.156*5.59^2

=17.05 rad or 2.714 rev

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