Two disks are mounted (like a merry-go-round) on low-friction bearings on the sa

Question

Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia 2.73 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 194 rev/min. The second disk, with rotational inertia 5.68 kg·m2 about its central axis, is set spinning counterclockwise at 690 rev/min. They then couple together. (a) What is their angular speed (rev/min) after coupling? (b) If instead the second disk is set spinning clockwise at 690 rev/min, what is their angular velocity (in rev/min, using the correct sign for direction) after they couple together?

Explanation / Answer

conservation of angular momentum ;

I1 1 + I2 2 = ( I1 + I2 )

( a )

2.73 * 194 + 5.68 * ( 690 ) = ( 2.73 + 5.68 ) ;

= 528.99 rev / min in the counterclocwise direction   

( b )

2.73 * 194 + 5.68 * ( - 690 ) = ( 2.73 + 5.68 ) ;

= -403.04 rev / min in the clockwise direction

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