Two disks are mounted (like a merry-go-round) on low-frictionbearings on the sam

Question

Two disks are mounted (like a merry-go-round) on low-frictionbearings on the same axle and can be brought together so that theycouple and rotate as one unit. The first disk, with rotationalinertia 4.31 kg·m2 about its central axis, is setspinning counterclockwise (which may be taken as the positivedirection) at 125 rev/min. The second disk, with rotational inertia7.93 kg·m2 about its central axis, is setspinning counterclockwise at 907 rev/min. They then coupletogether. (a) What is their angular speed(rev/min) after coupling? (b) If instead thesecond disk is set spinning clockwise at 907 rev/min, what is theirangular velocity (in rev/min, using the correct sign for direction)after they couple together?

Explanation / Answer

Data:
First disc:
     I1 = 4.31 kg.m2
     1 = 125rev/min
second disk:
   I2 = 7.93 kg-m2
   2 = 907 rev/min  
(a) Applying conservation of angular momentum
                      I1* 1 +I2*2 = (I1 + I2)*
              ==> = ( I1*1 +I2*2 ) / (I1 +I2)
   = (4.31 * 125 + 7.93 * 907) /(4.31 + 7.93)
   =   631.63 rev/min                          

                                    

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